**Memoirs of the American Mathematical Society**

2015;
107 pp;
Softcover

MSC: Primary 45; 35;

Print ISBN: 978-1-4704-1434-4

Product Code: MEMO/238/1124

List Price: $80.00

Individual Member Price: $48.00

**Electronic ISBN: 978-1-4704-2611-8
Product Code: MEMO/238/1124.E**

List Price: $80.00

Individual Member Price: $48.00

# On the Theory of Weak Turbulence for the Nonlinear Schrödinger Equation

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*M. Escobedo; J. J. L. Velázquez*

The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger 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

# Table of Contents

## On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation

- Cover Cover11 free
- Title page i2 free
- Chapter 1. Introduction 18 free
- Chapter 2. Well-Posedness Results 916
- 2.1. Weak solutions with interacting condensate 916
- 2.2. Weak solutions with non interacting condensate 1118
- 2.3. Mild solutions 1219
- 2.4. Existence of bounded mild solutions \index{mild solution} 1724
- 2.5. Existence of global weak solutions with interacting condensate \index{weak solution} 1825
- 2.6. Stationary solutions 2532
- 2.7. Weak solutions with non interacting condensate 2835

- Chapter 3. Qualitative behaviors of the solutions 3946
- Chapter 4. Solutions without condensation: Pulsating behavior 6774
- Chapter 5. Heuristic arguments and open problems 9198
- Chapter 6. Auxiliary results 99106
- Bibliography 103110
- Index 107114 free
- Back Cover Back Cover1120