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

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.

Show me the PDF file (236K), TEX file, and other files for this article.

James Colliander
Department of Mathematics, University of California
Berkeley, California, 94720-3840 USA
e-mail: colliand@math.berkeley.edu
Markus Keel
Department of Mathematics
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

Return to the EJDE web page