Mass Concentration for the Davey-Stewartson System

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 Schr\"{o}dinger equation. We also prove a mass concentration result for $L^{2}$-solutions.