On the local regularity of the KP-I equation in anisotropic Sobolev space
| dc.creator | Guo, Zihua | |
| dc.creator | Peng, Lizhong | |
| dc.creator | Wang, Baoxiang | |
| dc.date | 2009-05-01 | |
| dc.date.accessioned | 2026-07-07T13:10:58Z | |
| dc.date.available | 2026-07-07T13:10:58Z | |
| dc.description | We prove that the KP-I initial-value problem \begin{eqnarray*} \begin{cases} \partial_tu+\partial_x^3u-\partial_x^{-1}\partial_y^2u+\partial_x(u^2/2)=0 {on}{\R}^2_{x,y}\times {\R}_t; u(x,y,0)=ϕ(x,y), \end{cases} \end{eqnarray*} is locally well-posed in the space \begin{eqnarray*} H^{1,0}(\R^2)=\{ϕ\in L^2(\R^2): \ \normϕ_{H^{1,0}(\R^2)}\approx\normϕ_{L^2}+\norm{\partial_xϕ}_{L^2}<\infty\}. \end{eqnarray*} | |
| dc.description | 23 pages, 0 figures, submitted | |
| dc.identifier | https://arxiv.org/abs/0905.0039 | |
| dc.identifier | http://arxiv.org/abs/0905.0039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229149 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.title | On the local regularity of the KP-I equation in anisotropic Sobolev space | |
| dc.type | text |