We consider the initial value problem of the fifth-order modified KdV equation on the Sobolev spaces.
where and 's are real. We show the local well-posedness 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 well-posedness; ill-posedness; mKdV hierarchy.
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| Soonsik Kwon |
Department of Mathematics, University of California
Los Angeles, CA 90095-1555, USA
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