American Institute of Mathematical Sciences

May  2009, 8(3): 913-922. doi: 10.3934/cpaa.2009.8.913

Sharp threshold of global existence for the generalized Davey-Stewartson system in $R^2$

 1 College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, China, China 2 Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088

Received  May 2008 Revised  October 2008 Published  February 2009

This paper is concerned with the generalized Davey-Stewartson system in $\mathbf R^2$ which appears as mathematical models for the evolution of shallow-water waves having one predominant direction of travel. We obtain a sharp threshold of blowing up and global existence to the Cauchy problem of the system by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow. Furthermore, we answer the question: How small are the initial data, the global solutions to the Cauchy problem of the system exist.
Citation: Zaihui Gan, Boling Guo, Jian Zhang. Sharp threshold of global existence for the generalized Davey-Stewartson system in $R^2$. Communications on Pure & Applied Analysis, 2009, 8 (3) : 913-922. doi: 10.3934/cpaa.2009.8.913
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