| Title:
|
A short note on $L^q$ theory for Stokes problem with a pressure-dependent viscosity (English) |
| Author:
|
Mácha, Václav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
317-329 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study higher local integrability of a weak solution to the steady Stokes problem. We consider the case of a pressure- and shear-rate-dependent viscosity, i.e., the elliptic part of the Stokes problem is assumed to be nonlinear and it depends on $p$ and on the symmetric part of a gradient of $u$, namely, it is represented by a stress tensor $T(Du,p):=\nu (p,|D|^2)D$ which satisfies $r$-growth condition with $r\in (1,2]$. In order to get the main result, we use Calderón-Zygmund theory and the method which was presented for example in the paper Caffarelli, Peral (1998). (English) |
| Keyword:
|
Stokes problem |
| Keyword:
|
$L^q$ theory |
| Keyword:
|
pressure-dependent viscosity |
| MSC:
|
35B65 |
| MSC:
|
35Q35 |
| MSC:
|
76D03 |
| idZBL:
|
Zbl 06604469 |
| idMR:
|
MR3519604 |
| DOI:
|
10.1007/s10587-016-0258-x |
| . |
| Date available:
|
2016-06-16T12:39:43Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145726 |
| . |
| Reference:
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