Existence and Stability of Steady-State Solutions with Finite Energy for the Navier-Stokes equation in the Whole Space
| dc.creator | Bjorland, Clayton | |
| dc.creator | Schonbek, Maria E. | |
| dc.date | 2007-11-27 | |
| dc.date | 2007-11-28 | |
| dc.date.accessioned | 2026-07-07T08:45:20Z | |
| dc.date.available | 2026-07-07T08:45:20Z | |
| dc.description | We consider the steady-state Navier-Stokes equation in the whole space $\mathbb{R}^3$ driven by a forcing function $f$. The class of source functions $f$ under consideration yield the existence of at least one solution with finite Dirichlet integral ($\|\nabla U\|_2<\infty$). Under the additional assumptions that $f$ is absent of low modes and the ratio of $f$ to viscosity is sufficiently small in a natural norm we construct solutions which have finite energy (finite $L^2$ norm). These solutions are unique among all solutions with finite energy and finite Dirichlet integral. The constructed solutions are also shown to be stable in the following sense: If $U$ is such a solution then any viscous, incompressible flow in the whole space, driven by $f$ and starting with finite energy, will return to $U$. | |
| dc.description | 22 pages, submitted | |
| dc.identifier | https://arxiv.org/abs/0711.4183 | |
| dc.identifier | http://arxiv.org/abs/0711.4183 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142933 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35B35, 35Q30, 76D05 | |
| dc.title | Existence and Stability of Steady-State Solutions with Finite Energy for the Navier-Stokes equation in the Whole Space | |
| dc.type | text |