On the fifth order KdV equation: local well-posedness and lack of uniform continuity of the solution map

Details On the fifth order KdV equation: local well-posedness and lack of uniform continuity of the solution map On the fifth order KdV equation: local well-posedness and lack of uniform continuity of the solution map

2007-08-29

arxiv.org/abs/0708.4010v1

Mathematics

Analysis of PDEs

30 pages

Scientific paper

In this paper we prove that the fifth order equation arising from the KdV
hierarchy $ \partial_tu + \partial_x^5u + c_1\partial_x u\partial_x^2u +
c_2u\partial_x^3u = 0 $ is locally well-posed in $ H^s(\mathbb{R}) $ for $ s>
5/2. Also, we prove the solution map of the equation is not uniformly
continuous for $s>0$.

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