| Title:
|
Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in $\Bbb R^n$ (English) |
| Author:
|
Farwig, R. |
| Author:
|
Sohr, H. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
61-79 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a bounded domain $\Omega \subset \Bbb R ^n$, $n\geq 3,$ we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system $-\Delta u + u \cdot \nabla u + \nabla p=f$, $\div u = k$, $u_{|_{\partial \Omega }}=g$ with $u \in L^q$, $q \geq n$, and very general data classes for $f$, $k$, $g$ such that $u$ may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of a series of papers by Frehse & Růžička, see e.g. Existence of regular solutions to the stationary Navier-Stokes equations, Math. Ann. 302 (1995), 669--717, where the existence of a weak solution which is locally regular is proved. (English) |
| Keyword:
|
stationary Stokes and Navier-Stokes system |
| Keyword:
|
very weak solutions |
| Keyword:
|
existence and uniqueness in higher dimensions |
| Keyword:
|
regularity classes in higher dimensions |
| MSC:
|
35B65 |
| MSC:
|
35J55 |
| MSC:
|
35J65 |
| MSC:
|
35Q30 |
| MSC:
|
76D05 |
| MSC:
|
76D07 |
| idZBL:
|
Zbl 1224.76034 |
| idMR:
|
MR2486616 |
| . |
| Date available:
|
2010-07-20T14:52:56Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140464 |
| . |
| Reference:
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