Dispersive Equations and Nonlinear Waves: Generalized by Herbert Koch,Daniel Tataru,Monica Vişan PDF

By Herbert Koch,Daniel Tataru,Monica Vişan

the 1st a part of the ebook offers an creation to key instruments and strategies in dispersive equations: Strichartz estimates, bilinear estimates, modulation and tailored functionality areas, with an program to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, international strategies to the defocusing challenge, and scattering are the point of interest of the second one half. utilizing this concrete instance, it walks the reader throughout the induction on power procedure, which has develop into the fundamental technique for tackling huge info severe difficulties. This contains refined/inverse Strichartz estimates, the life and virtually periodicity of minimum blow up options, and the advance of long-time Strichartz inequalities. The 3rd half describes wave and Schrödinger maps. beginning through construction heuristics approximately multilinear estimates, it offers a close define of this very lively zone of geometric/dispersive PDE. It makes a speciality of ideas and ideas and may offer graduate scholars with a stepping stone to this intriguing path of research.

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Dispersive Equations and Nonlinear Waves: Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps (Oberwolfach Seminars) by Herbert Koch,Daniel Tataru,Monica Vişan


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