Mass Concentration for the Davey-Stewartson System

Abstract

This paper is concerned with the analysis of blow-up solutions to the elliptic-elliptic Davey-Stewartson system, which appears in the description of the evolution of surface water waves. We prove a mass concentration property for $H^1$-solutions, analogous to the one known for the $L^2$-critical nonlinear Schrödinger equation. We also prove a mass concentration result for $L^2$-solutions.

18 pages