Large data local well-posedness for a class of dispersive equations

Details Large data local well-posedness for a class of dispersive equations Large data local well-posedness for a class of dispersive equations

2011-10-25

arxiv.org/abs/1110.5402v1

Mathematics

Analysis of PDEs

Scientific paper

In this article we consider the Cauchy problem with large initial data for an equation of the form (\partial_t+\partial_x^3)u=F(u,u_x,u_{xx}) where F is a polynomial with no constant or linear terms. Local well-posedness was established in weighted Sobolev spaces by Kenig-Ponce-Vega. In this paper we prove local well-posedness in a translation invariant subspace of H^s by adapting the result of Marzuola-Metcalfe-Tataru on quasilinear Schrodinger equations.

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