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

2011/10/25 by Benjamin Harrop‐Griffiths, Benjamin Harrop-Griffiths, Harrop-Griffiths, Benjamin
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #math.AP

paper · pdf · doi:10.48550/arxiv.1110.5402

21 pages. Some typos corrected, references updated

openalex publication_date 2011/10/25 · arxiv created 2013/06/24 · arxiv updated 2013/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we consider the Cauchy problem with large initial data 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. 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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