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Long time bounds for the periodic KP-II equation. (English) Zbl 1073.35195

It is shown that Bourgain’s result concerning the existence of a unique global-in-time solution of the KP-II equation may be generalized for a time of \(\varepsilon^{-2}\) order.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35B40 Asymptotic behavior of solutions to PDEs
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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