On the theory of weak turbulence for the nonlinear Schrödinger equation
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Bibliographic Information
On the theory of weak turbulence for the nonlinear Schrödinger equation
（Memoirs of the American Mathematical Society, v. 238,
American Mathematical Society, 2015
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Note
Bibliography: p. 103-105
Includes index
Description and Table of Contents
Description
The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrodinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.
Table of Contents
Introduction
Well-posedness results
Qualitative behaviors of the solutions
Solutions without condensation: Pulsating behavior
Heuristic arguments and open problems
Auxiliary results
Bibliography
Index
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