Large data local well-posedness for a class of KdV-type equations II

2013/06/24 by Benjamin Harrop-Griffiths, Harrop-Griffiths, Benjamin
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1306.5791

25 pages

arxiv created 2013/06/24 · arxiv updated 2013/06/26

Abstract

We consider the Cauchy problem for an equation of the form ∂_t+∂_x³)u=F(u,u_x,u_xx) where F is a polynomial with no constant or linear terms and no quadratic uu_xx term. For a polynomial nonlinearity with no quadratic terms, Kenig-Ponce-Vega proved local well-posedness in H^s for large s. In this paper we prove local well-posedness in low regularity Sobolev spaces and extend the result to certain quadratic nonlinearities. The result is based on spaces and estimates similar to those used by Marzuola-Metcalfe-Tataru for quasilinear Schrodinger equations.

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