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Local and Global Analysis of Nonlinear Dispersive and Wave Equations (CBMS Regional Conference Series in Mathematics)

Local And Global Analysis of Nonlinear Dispersive And Wave Equations

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Local and Global Analysis of Nonlinear Dispersive and Wave Equations (CBMS Regional Conference Series in Mathematics)

Local And Global Analysis of Nonlinear Dispersive And Wave Equations

4.85 91,385 ratings · 3,222 reviews
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Overview: Among nonlinear PDEs, dispersive and wave equations form an important class of equations. These include the nonlinear Schrodinger equation, the nonlinear wave equation, the Korteweg de Vries equation, and the wave maps equation. This book is an introduction to the methods and results used in the modern analysis (both locally and globally in time) of the Cauchy problem for such equations. Starting only with a basic knowledge of graduate real analysis and Fourier analysis, the text first presents basic nonlinear tools such as the bootstrap method and perturbation theory in the simpler context of nonlinear ODE, then introduces the harmonic analysis and geometric tools used to control linear dispersive PDE. These methods are then combined to study four model nonlinear dispersive equations. Through extensive exercises, diagrams, and informal discussion, the book gives a rigorous theoretical treatment of the material, the real-world intuition and heuristics that underlie the subject, as well as mentioning connections with other areas of PDE, harmonic analysis, and dynamical systems. As the subject is vast, the book does not attempt to give a comprehensive survey of the field, but instead concentrates on a representative sample of results for a selected set of equations, ranging from the fundamental local and global existence theorems to very recent results, particularly focusing on the recent progress in understanding the evolution of energy-critical dispersive equations from large data. The book is suitable for a graduate course on nonlinear PDE.

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Book details & editions

ISBN
996239
Publication date
July 1, 2006
Language
Eng
Pages
N/A pages
Reading Options
PDF · EPUB · Mobi
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Terence Tao
About the Author
Terence Tao
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Terence Tao writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. Terence Tao lives with their spouse and a very vocal rescue cat.

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George Young
George Young November 23, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Andrew Campbell March 14, 2025
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Linda Hill May 05, 2024
A decent, if standard, experience. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. A fair 3 stars.
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. Suitable if your reading queue is empty.
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
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An acceptable diversion. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perhaps more aligned with a different audience's tastes.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
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Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Ryan Robinson
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
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Nancy Harris December 18, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Emily Thompson
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I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Ryan  Parker
Ryan Parker August 29, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Thomas Carter
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Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Robert Ramirez
Robert Ramirez August 25, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Kimberly Phillips
Kimberly Phillips October 29, 2025
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
George Nguyen
George Nguyen August 18, 2024
An acceptable diversion. The prose was competent, yet the characters lacked the depth I usually seek. Unlikely to reread, but a reasonable expenditure of time.
Donna Gomez
Donna Gomez July 26, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Nancy Gonzalez
Nancy Gonzalez September 23, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Kevin Garcia
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
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Margaret Sanchez October 12, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Michelle Clark
Michelle Clark September 09, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Jessica Torres
Jessica Torres August 30, 2024
Not entirely to my refined tastes. The prose was competent, yet the characters lacked the depth I usually seek. Unlikely to reread, but a reasonable expenditure of time.
John Rivera
John Rivera March 12, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Kimberly Brown
Kimberly Brown June 15, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Betty Thomas
Betty Thomas July 08, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Susan Wright
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Andrew Edwards
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Rebecca Nguyen
Rebecca Nguyen January 07, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Sandra Jones
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A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Brian Martinez July 27, 2024
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
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Linda Nelson October 08, 2025
A decent, if standard, experience. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time.
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Melissa Lee January 03, 2024
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Barbara Allen
Barbara Allen October 11, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Kenneth Lopez
Kenneth Lopez February 01, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Barbara Rodriguez
Barbara Rodriguez May 21, 2025
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Ryan Clark
Ryan Clark November 16, 2025
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Donna Anderson
Donna Anderson February 11, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Deborah Gomez
Deborah Gomez December 10, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Lisa  Davis
Lisa Davis September 02, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Thomas Smith
Thomas Smith November 18, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Barbara Johnson
Barbara Johnson March 29, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Kevin Thomas
Kevin Thomas October 07, 2025
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Donald Hill
Donald Hill July 19, 2024
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Anthony Martinez
Anthony Martinez March 16, 2025
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
John Sanchez
John Sanchez July 23, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Joshua Evans
Joshua Evans February 26, 2024
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Lisa Ramirez
Lisa Ramirez October 15, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Melissa Hill
Melissa Hill May 22, 2024
A decent, if standard, experience. It verged on repetitive in the second act. A more concise edit would have served it well. Perhaps more aligned with a different audience's tastes.
Rebecca Hill
Rebecca Hill July 10, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Jennifer Roberts
Jennifer Roberts July 15, 2024
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Stephanie Allen
Stephanie Allen June 16, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
John Mitchell
John Mitchell January 16, 2024
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Joshua Lopez
Joshua Lopez October 13, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Emily Ramirez
Emily Ramirez October 23, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Linda Hill
Linda Hill February 11, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Elizabeth Martinez
Elizabeth Martinez May 03, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
David Baker
David Baker March 01, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Nancy Flores
Nancy Flores November 02, 2025
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Thomas  Davis
Thomas Davis April 20, 2025
I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. Unlikely to reread, but a reasonable expenditure of time.
Patricia Baker
Patricia Baker July 10, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Sarah Sanchez
Sarah Sanchez December 08, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Gary Thompson
Gary Thompson September 22, 2025
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Sharon Flores
Sharon Flores August 19, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Dorothy Robinson
Dorothy Robinson May 17, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Lisa  Davis
Lisa Davis August 23, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Amanda Sanchez
Amanda Sanchez June 30, 2024
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Kevin Carter
Kevin Carter June 18, 2025
I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perfectly average.
Thomas Carter
Thomas Carter June 02, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
William Lopez
William Lopez July 13, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Michelle Turner
Michelle Turner November 01, 2025
It was adequate. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perfectly average.
Kevin Garcia
Kevin Garcia March 02, 2024
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Cynthia Thompson
Cynthia Thompson February 26, 2025
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
John Sanchez
John Sanchez May 06, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Ashley Torres
Ashley Torres July 15, 2024
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Rebecca Nguyen
Rebecca Nguyen July 21, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Anthony Rodriguez
Anthony Rodriguez August 01, 2025
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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