Global solutions for 2D quadratic Schrodinger equations

2010/01/28 by Germain, Pierre, Masmoudi, Nader, Shatah, Jalal · 5 citations
#35Q41 #42B37 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1001.5158

Abstract

We prove global existence and scattering for a class of quadratic Schrodinger equations in dimension 2. The proof relies on the idea of space-time resonance.

Cited by

• Space-time resonances in the spatiotemporal spectrum of nonlinear dispersive waves
• Global existence and decay of small solutions in a viscous half Klein-Gordon equation
• Global well-posedness and scattering for the 2D modified Zakharov-Kuznetsov equation
• Scattering of the 2D modified Zakharov-Kuznetsov equation
• Large Time Behavior of the Klein-Gordon-Schrödinger system

Related

• Global Solutions For Systems of Quadratic Nonlinear Schrödinger Equations in 3D
• Global solutions to 3D quadratic nonlinear Schrödinger-type equation
• Global existence without decay for quadratic Klein-Gordon equations
• Global Solutions for 5D Quadratic Fourth-Order Schrödinger Equations
• Scattering for quadratic-type Schr "odinger systems in dimension five\n without mass-resonance