On the ill-posedness of the Gardner equation.

Miguel Angel Alejo Plana

doi:10.1016/j.jmaa.2012.06.018

On the ill-posedness of the Gardner equation.

Miguel Angel Alejo Plana

Department of Mathematical Sciences

8 Citations (Scopus)

Abstract

We present ill-posedness results for the initial value problem (IVP) for the Gardner equation. We measure the regularity of the Cauchy problem in the classical Sobolev spaces Hs, and show the critical Sobolev index under which the local well-posedness of the problem is not present, in the sense that the dependence of solutions upon initial data fails to be continuous.

Original language	English
Journal	Journal of Mathematical Analysis and Applications
Volume	396
Issue number	1
Pages (from-to)	256-260
ISSN	0022-247X
DOIs	https://doi.org/10.1016/j.jmaa.2012.06.018
Publication status	Published - 1 Dec 2012

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10.1016/j.jmaa.2012.06.018

Cite this

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title = "On the ill-posedness of the Gardner equation.",

abstract = "We present ill-posedness results for the initial value problem (IVP) for the Gardner equation. We measure the regularity of the Cauchy problem in the classical Sobolev spaces Hs, and show the critical Sobolev index under which the local well-posedness of the problem is not present, in the sense that the dependence of solutions upon initial data fails to be continuous.",

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AB - We present ill-posedness results for the initial value problem (IVP) for the Gardner equation. We measure the regularity of the Cauchy problem in the classical Sobolev spaces Hs, and show the critical Sobolev index under which the local well-posedness of the problem is not present, in the sense that the dependence of solutions upon initial data fails to be continuous.

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