Liouville type of theorems for the Euler and the Navier-Stokes equations
| dc.creator | Chae, Dongho | |
| dc.date | 2008-09-04 | |
| dc.date | 2008-09-25 | |
| dc.date.accessioned | 2026-07-07T10:04:50Z | |
| dc.date.available | 2026-07-07T10:04:50Z | |
| dc.description | We prove Liouville type of theorems for weak solutions of the Navier-Stokes and the Euler equations. In particular, if the pressure satisfies $ p\in L^1 (0,T; L^1 (\Bbb R^N))$ with $\int_{\Bbb R^N} p(x,t)dx \geq 0$, then the corresponding velocity should be trivial, namely $v=0$ on $\Bbb R^N \times (0,T)$. In particular, this is the case when $p\in L^1 (0,T; \mathcal{H}^1 (\Bbb R^N))$, where $\mathcal{H}^1 (\Bbb R^N)$ the Hardy space. On the other hand, we have equipartition of energy over each component, if $p\in L^1 (0,T; L^1 (\Bbb R^N))$ with $\int_{\Bbb R^N} p(x,t)dx <0$. Similar results hold also for the magnetohydrodynamic equations. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/0809.0743 | |
| dc.identifier | http://arxiv.org/abs/0809.0743 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169827 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q30, 35Q35, 76Dxx, 76Bxx | |
| dc.title | Liouville type of theorems for the Euler and the Navier-Stokes equations | |
| dc.type | text |