Global well-posedness and limit behavior for the modified finite-depth-fluid equation
| dc.creator | Guo, Zihua | |
| dc.creator | Wang, Baoxiang | |
| dc.date | 2008-09-13 | |
| dc.date.accessioned | 2026-07-07T10:02:45Z | |
| dc.date.available | 2026-07-07T10:02:45Z | |
| dc.description | Considering the Cauchy problem for the modified finite-depth-fluid equation $\partial_tu-\G_δ(\partial_x^2u)\mp u^2u_x=0, u(0)=u_0$, where $\G_δf=-i \ft ^{-1}[\coth(2πδξ)-\frac{1}{2πδξ}]\ft f$, $δ\ges 1$, and $u$ is a real-valued function, we show that it is uniformly globally well-posed if $u_0 \in H^s (s\geq 1/2)$ with $\norm{u_0}_{L^2}$ sufficiently small for all $δ\ges 1$. Our result is sharp in the sense that the solution map fails to be $C^3$ in $H^s (s<1/2)$. Moreover, we prove that for any $T>0$, its solution converges in $C([0,T]; H^s)$ to that of the modified Benjamin-Ono equation if $δ$ tends to $+\infty$. | |
| dc.description | 29 pages, 0 figures | |
| dc.identifier | https://arxiv.org/abs/0809.2318 | |
| dc.identifier | http://arxiv.org/abs/0809.2318 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169082 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35Q35; 35Q53 | |
| dc.title | Global well-posedness and limit behavior for the modified finite-depth-fluid equation | |
| dc.type | text |