WELL-POSEDNESS AND ILL-POSEDNESS OF THE FIFTH-ORDER MODIFIED KDV EQUATION

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We consider the initial value problem of the fifth-order modified KdV equation on the Sobolev spaces. partial derivative(t)u - partial derivative(5)(x)u + c(1)partial derivative(3)(x)(u(3)) + c(2)u partial derivative(x)u partial derivative(2)(x)u + c(3)uu partial derivative(3)(x)u = 0 u(x,0) = u(0)(x) where u : R x R -> R and c(j)'s are real. We show the local well-posedness in H-s(R) for s >= 3/4 via the contraction principle on X-s,X-b space. Also, we show that the solution map from data to the solutions fails to be uniformly continuous below H-3/4(R). The counter example is obtained by approximating the fifth order mKdV equation by the cubic NLS equation.
Publisher
TEXAS STATE UNIV
Issue Date
2008
Language
English
Article Type
Article
Citation

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS

ISSN
1072-6691
URI
http://hdl.handle.net/10203/93205
Appears in Collection
MA-Journal Papers(저널논문)
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