We consider the long time well-posedness of the Cauchy problem with large Sobolev data for a class of nonlinear Schrödinger equations (NLS) on R2 with power nonlinearities of arbitrary odd degree. Specifically, the method in this paper applies to those NLS equations having either elliptic signature with a defocusing nonlinearity, or else having an indefinite signature. By rigorously justifying that these equations govern the modulation of wave packet-like solutions to an artificially constructed equation with an advantageous structure, we show that a priori every subcritical inhomogeneous Sobolev norm of the solution increases at most polynomially in time. Global well-posedness follows by a standard application of the subcritical local theory.
ASJC Scopus subject areas
- Applied Mathematics