Global low-regularity solutions for Kadomtsev-Petviashvili equation. (English) Zbl 0977.35125

Tzvetkov, N.

Differ. Integral Equ. 13, No. 10-12, 1289-1320 (2000).

Summary: We study the initial-value problem for the KP-II equation. We prove the existence of solutions to the integral equation corresponding to KP-II for any data in \(L^2\), removing the additional condition imposed in a previous paper [author, Commun. Partial Differ. Equations 24, No. 7-8, 1367-1397 (1999; Zbl 0934.35161)]. Following a method recently developed by J. Bourgain we obtain global solutions to KP-II with data below \(L^2\).

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
37K45	Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
35B65	Smoothness and regularity of solutions to PDEs

Keywords:

nonsmooth data; initial value problem; KP-II equation; existence; global solutions

Citations:

Zbl 0934.35161