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Blow-up dynamics of L 2 solutions for the Davey-Stewartson system

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Abstract

We study the blow-up solutions for the Davey-Stewartson system (D-S system, for short) in L 2 x (ℝ2). First, we give the nonlinear profile decomposition of solutions for the D-S system. Then, we prove the existence of minimal mass blow-up solutions. Finally, by using the characteristic of minimal mass blow-up solutions, we obtain the limiting profile and a precisely mass concentration of L 2 blow-up solutions for the D-S system.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan Normal University, Chengdu, 610066, P. R. China

    Shi Hui Zhu

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  1. Shi Hui Zhu
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Correspondence to Shi Hui Zhu.

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Supported by National Natural Science Foundation of China (Grant No. 11371267) and Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20125134120001)

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Zhu, S.H. Blow-up dynamics of L 2 solutions for the Davey-Stewartson system. Acta. Math. Sin.-English Ser. 31, 411–429 (2015). https://doi.org/10.1007/s10114-015-4349-7

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  • DOI: https://doi.org/10.1007/s10114-015-4349-7

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