Large data local well-posedness for a class of KdV-type equations
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- by Benjamin Harrop-Griffiths PDF
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Abstract:
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 Schrödinger equations.References
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Additional Information
- Benjamin Harrop-Griffiths
- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- MR Author ID: 1086344
- ORCID: 0000-0002-0215-7613
- Email: benhg@math.berkeley.edu
- Received by editor(s): March 5, 2012
- Received by editor(s) in revised form: May 15, 2012
- Published electronically: October 3, 2014
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 755-773
- MSC (2010): Primary 35Q53, 35G25
- DOI: https://doi.org/10.1090/S0002-9947-2014-05882-0
- MathSciNet review: 3280026