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Mass concentration for the Davey-Stewartson system. (English) Zbl 1240.35520
Summary: 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.
MSC:
35Q55NLS-like (nonlinear Schrödinger) equations
76B15Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35J47Second-order elliptic systems
35J60Nonlinear elliptic equations
35B44Blow-up (PDE)