Electron. J. Diff. Eqns., Vol. 2001(2001), No. 26, pp. 1-7.

Global well-posedness for KdV in Sobolev spaces of negative index

J. Colliander, M. Keel, G. Staffilani, H. Takaoka, & T. Tao

Abstract:
The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data. In particular, we show global well-posedness for initial data in $H^s(\mathbb{R})$ for -3/10 < s.

Submitted January 31, 2001. Published April 27, 2001.
Math Subject Classifications: 35Q53, 42B35, 37K10.
Key Words: Korteweg-de Vries equation, nonlinear dispersive equations, bilinear estimates.

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James Colliander
Department of Mathematics, University of California
Berkeley, California, 94720-3840 USA
e-mail: colliand@math.berkeley.edu
Markus Keel
Department of Mathematics
Caltech
Pasadena, California, 91125, USA
e-mail: keel@cco.caltech.edu
Gigliola Staffilani
Department of Mathematics
Stanford University
Stanford, California, 94305, USA
e-mail: gigliola@math.stanford.edu
Hideo Takaoka
Division of Mathematics, Graduate School of Science
Hokkaido University
Sapporo, 060-0810, Japan.
e-mail: takaoka@math.sci.hokudai.ac.jp
Terence Tao
Department of Mathematics
University of California,
Los Angeles, California, 90095-1596, USA
e-mail: tao@math.ucla.edu

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