A-priori bounds for the 1-d cubic NLS in negative Sobolev spaces

Abstract

We consider the cubic Nonlinear Schrodinger Equation in one space dimension, either focusing or defocusing. We prove that the solutions satisfy a-priori local in time H^s bounds in terms of the H^s size of the initial data for s greater than or equal to -1/6.

27 pages very minor misprints corrected (see formulas (4), (7))

References in corpus (1)

• A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order

Cited by in corpus (1)

• Global wellposedness in the energy space for the Maxwell-Schrödinger system