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A cross-constrained variational problem for the generalized Davey–Stewartson system
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 52 / Issue 1 / February 2009
- Published online by Cambridge University Press:
- 02 February 2009, pp. 67-77
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- Article
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We study the sharp threshold for blow-up and global existence and the instability of standing wave eiωtuω(x) for the Davey–Stewartson system
in ℝ3, where uω is a ground state. By constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow, we derive a sharp criterion for global existence and blow-up of the solutions to (DS), which can be used to show that there exist blow-up solutions of (DS) arbitrarily close to the standing waves.
