Electron. J. Diff. Eqns.,
Vol. 2008(2008), No. 01, pp. 115.
Wellposedness and illposedness of the fifthorder
modified KdV equation
Soonsik Kwon
Abstract:
We consider the initial value problem of the fifthorder modified
KdV equation on the Sobolev spaces.
where
and
's
are real. We show the local wellposedness in
for
via the contraction principle on
space. Also, we show that the solution map from data to the
solutions fails to be uniformly continuous below
. The counter example is obtained by
approximating the fifth order mKdV equation by the cubic NLS
equation.
Submitted November 7, 2007. Published January 2, 2008.
Math Subject Classifications: 35Q53.
Key Words: Local wellposedness; illposedness; mKdV hierarchy.
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Soonsik Kwon
Department of Mathematics, University of California
Los Angeles, CA 900951555, USA
email: rhex2@math.ucla.edu

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