The Navier-Stokes problem modified by an absorption term
| dc.creator | de Oliveira, Hermenegildo Borges | |
| dc.date | 2009-03-31 | |
| dc.date.accessioned | 2026-07-07T12:58:37Z | |
| dc.date.available | 2026-07-07T12:58:37Z | |
| dc.description | In this work we consider the Navier-Stokes problem modified by the absorption term $|\textbf{u}|^{σ-2}\textbf{u}$, where $σ>1$, which is introduced in the momentum equation. % For this new problem, we prove the existence of weak solutions for any dimension $N\geq 2$ and its uniqueness for N=2. % Then we prove that, for zero body forces, the weak solutions extinct in a finite time if $1<σ<2$, exponentially decay in time if $σ=2$ and decay with a power-time rate if $σ>2$. % We prove also that for a general non-zero body forces, the weak solutions exponentially decay in time for any $σ>1$. In the special case of a suitable forces field which vanishes at some instant, we prove that the weak solutions extinct at the same instant provided $1<σ<2$. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/0903.5513 | |
| dc.identifier | http://arxiv.org/abs/0903.5513 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/225304 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35Q30, 76D03, 35B40 | |
| dc.title | The Navier-Stokes problem modified by an absorption term | |
| dc.type | text |