Liouville type of theorems with weights for the Navier-Stokes equations and the Euler equations
| dc.creator | Chae, Dongho | |
| dc.date | 2008-11-28 | |
| dc.date | 2009-01-02 | |
| dc.date.accessioned | 2026-07-07T12:23:28Z | |
| dc.date.available | 2026-07-07T12:23:28Z | |
| dc.description | We study Liouville type of theorems for the Navier-Stokes and the Euler equations on $\Bbb R^N$, $N\geq 2$. Specifically, we prove that if a weak solution $(v,p)$ satisfies $|v|^2 +|p| \in L^1 (0,T; L^1(\Bbb R^N, w_1(x)dx))$ and $\int_{\Bbb R^N} p(x,t)w_2 (x)dx \geq0$ for some weight functions $w_1(x)$ and $w_2 (x)$, then the solution is trivial, namely $v=0$ almost everywhere on $\Bbb R^N \times (0, T)$. Similar results hold for the MHD Equations on $\Bbb R^N$, $N\geq3$. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/0811.4647 | |
| dc.identifier | http://arxiv.org/abs/0811.4647 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/214001 | |
| dc.subject | Analysis of PDEs | |
| dc.title | Liouville type of theorems with weights for the Navier-Stokes equations and the Euler equations | |
| dc.type | text |