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Zbl 1126.35069
Shu, Ji; Zhang, Jian
Sharp conditions of global existence for the generalized Davey-Stewartson system. (English)
[J] IMA J. Appl. Math. 72, No. 1, 36-42 (2007). ISSN 0272-4960; ISSN 1464-3634/e

Summary: This paper discusses the generalized Davey-Stewartson system. By constructing a cross-constrained variational problem and so-called invariant manifolds of the evolution flow, we derive a sharp criterion for blow-up and global existence of the solutions.

MSC 2000:: *35Q55 NLS-like (nonlinear Schroedinger) equations
35B40 Asymptotic behavior of solutions of PDE
47J30 Variational methods
58E05 Abstract critical point theory

Keywords: cross-constrained variational problem; global existence; blow-up

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