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

Abstract

In this paper we prove that the fifth order equation arising from the KdV hierarchy ${\partial }_{t}u+{\partial }_x^{5}u+c_1{\partial }_{x}u{\partial }_x^{2}u+c_{2}u{\partial }_x^{3}u=0$ is locally well-posed in $H^s(\mathbb{R})$ for $s>5/2.Also,weprovethesolutionmapoftheequationisnotuniformlycontinuousfor$s>0$.

30 pages

References in corpus (1)

• Nonlinear wave interactions for the Benjamin-Ono equation