Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations
| dc.creator | Vento, Stéphane | |
| dc.date | 2008-02-07 | |
| dc.date.accessioned | 2026-07-07T09:19:18Z | |
| dc.date.available | 2026-07-07T09:19:18Z | |
| dc.description | We study the Cauchy problem for the dissipative Benjamin-Ono equations $u_t+\H u_{xx}+|D|^αu+uu_x=0$ with $0\leqα\leq 2$. When $0\leqα< 1$, we show the ill-posedness in $H^s(\R)$, $s\in\R$, in the sense that the flow map $u_0\mapsto u$ (if it exists) fails to be $\C^2$ at the origin. For $1<α\leq 2$, we prove the global well-posedness in $H^s(\R)$, $s>-α/4$. It turns out that this index is optimal. | |
| dc.identifier | https://arxiv.org/abs/0802.1039 | |
| dc.identifier | http://arxiv.org/abs/0802.1039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154344 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q55, 35A05, 35M10 | |
| dc.title | Well-posedness and ill-posedness results for dissipative Benjamin-Ono equations | |
| dc.type | text |