On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation

ISBN-13: 9781470414344 / Angielski

M. Escobedo;J. J. L. Velazquez

Opis

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.

Spis treści

• Introduction
• Well-posedness results
• Qualitative behaviors of the solutions
• Solutions without condensation: Pulsating behavior
• Heuristic arguments and open problems
• Auxiliary results
• Bibliography
• Index