| Title:
|
Cauchy problem for the non-newtonian viscous incompressible fluid (English) |
| Author:
|
Pokorný, Milan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
41 |
| Issue:
|
3 |
| Year:
|
1996 |
| Pages:
|
169-201 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the Cauchy problem for the non-Newtonian incompressible fluid with the viscous part of the stress tensor $\tau ^V(\mathbb{e}) = \tau (\mathbb{e}) - 2\mu _1 \Delta \mathbb{e}$, where the nonlinear function $\tau (\mathbb{e})$ satisfies $\tau _{ij}(\mathbb{e})e_{ij} \ge c|\mathbb{e}|^p$ or $\tau _{ij}(\mathbb{e})e_{ij} \ge c(|\mathbb{e}|^2+|\mathbb{e}|^p)$. First, the model for the bipolar fluid is studied and existence, uniqueness and regularity of the weak solution is proved for $p > 1$ for both models. Then, under vanishing higher viscosity $\mu _1$, the Cauchy problem for the monopolar fluid is considered. For the first model the existence of the weak solution is proved for $p > \frac{3n}{n+2}$, its uniqueness and regularity for $p \ge 1 + \frac{2n}{n+2}$. In the case of the second model the existence of the weak solution is proved for $p>1$. (English) |
| Keyword:
|
non-Newtonian incompressible fluids |
| Keyword:
|
Navier-Stokes equations |
| Keyword:
|
Cauchy problem |
| MSC:
|
35Q30 |
| MSC:
|
76A05 |
| idZBL:
|
Zbl 0863.76003 |
| idMR:
|
MR1382464 |
| DOI:
|
10.21136/AM.1996.134320 |
| . |
| Date available:
|
2009-09-22T17:51:01Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134320 |
| . |
| Reference:
|
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