Well-posedness and ill-posedness of the fifth order modifed KdV equation
| dc.creator | Kwon, Soonsik | |
| dc.date | 2007-11-07 | |
| dc.date.accessioned | 2026-07-07T08:41:20Z | |
| dc.date.available | 2026-07-07T08:41:20Z | |
| dc.description | We consider the initial value problem of the fifth order modified KdV equation on the Sobolev spaces. \partial_t u - \partial_x^5u + c_1\partial_x^3(u^3) + c_2u\partial_x u\partial_x^2 u + c_3uu\partial_x^3 u =0, u(x,0)= u_0(x) where $ u:R\timesR \to R $ and $c_j$'s are real. We show the local well-posedness in H^s(R) for s \geq 3/4 via the contraction principle on $X^{s,b}$ 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. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/0711.1060 | |
| dc.identifier | http://arxiv.org/abs/0711.1060 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141647 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35J53 | |
| dc.title | Well-posedness and ill-posedness of the fifth order modifed KdV equation | |
| dc.type | text |