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Zbl 1240.35520
Richards, Geordie
Mass concentration for the Davey-Stewartson system. (English)
[J] Differ. Integral Equ. 24, No. 3-4, 261-280 (2011). ISSN 0893-4983

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 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
76B15 Wave motions (fluid mechanics)
35J47
35J60 Nonlinear elliptic equations
35B44

Keywords: elliptic-elliptic Davey-Stewartson system; blow-up; mass concentration

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Zentralblatt MATH Berlin [Germany]