Quasilinear Schrödinger equations I: Small data and quadratic interactions

Details Quasilinear Schrödinger equations I: Small data and quadratic interactions Quasilinear Schrödinger equations I: Small data and quadratic interactions

2011-06-02

arxiv.org/abs/1106.0490v1

Mathematics

Analysis of PDEs

25 pages, 0 figures

Scientific paper

In this article we prove local well-posedness in low-regularity Sobolev spaces for general quasilinear Schr\"odinger equations. These results represent improvements of the pioneering works by Kenig-Ponce-Vega and Kenig-Ponce-Rolvung-Vega, where viscosity methods were used to prove existence of solutions in very high regularity spaces. Our arguments here are purely dispersive. The function spaces in which we show existence are constructed in ways motivated by the results of Mizohata, Ichinose, Doi, and others, including the authors.

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