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


Author: Benjamin Harrop-Griffiths
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
Published electronically: October 3, 2014
MathSciNet review: 3280026
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Abstract: In this article we consider the Cauchy problem with large initial data for an equation of the form

$\displaystyle (\partial _t+\partial _x^3)u=F(u,u_x,u_{xx})$

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.

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Additional Information

Benjamin Harrop-Griffiths
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: benhg@math.berkeley.edu

DOI: https://doi.org/10.1090/S0002-9947-2014-05882-0
Received by editor(s): March 5, 2012
Received by editor(s) in revised form: May 15, 2012
Published electronically: October 3, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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