| Title:
|
On the exterior problem in 2D for stationary flows of fluids with shear dependent viscosity (English) |
| Author:
|
Bildhauer, M. |
| Author:
|
Fuchs, M. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
221-236 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
On the complement of the unit disk $B$ we consider solutions of the equations describing the stationary flow of an incompressible fluid with shear dependent viscosity. We show that the velocity field $u$ is equal to zero provided $u|_{\partial B} = 0$ and $\lim_{|x| \to \infty} |x|^{1/3} |u (x)| = 0$ uniformly. For slow flows the latter condition can be replaced by $\lim_{|x| \to \infty} |u (x)| = 0$ uniformly. In particular, these results hold for the classical Navier-Stokes case. (English) |
| Keyword:
|
equations of Navier-Stokes type |
| Keyword:
|
stationary case |
| Keyword:
|
exterior problem in 2D |
| MSC:
|
35Q30 |
| MSC:
|
76D05 |
| idZBL:
|
Zbl 1265.35257 |
| idMR:
|
MR3017256 |
| . |
| Date available:
|
2012-08-08T08:59:48Z |
| Last updated:
|
2014-07-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142886 |
| . |
| Reference:
|
[BF] Bildhauer M., Fuchs M.: Variational integrals of splitting type: higher integrability under general growth conditions.Ann. Mat. Pura Appl. 188 (2009), 467–496. Zbl 1181.49035, MR 2512159, 10.1007/s10231-008-0085-2 |
| Reference:
|
[Fu] Fuchs M.: Liouville theorems for stationary flows of shear thickening fluids in the plane.J. Math. Fluid Mech. DOI 10.1007/s00021-011-0070-1. |
| Reference:
|
[FuSe] Fuchs M., Seregin G.A.: Variational methods for problems from plasticity theory and for generalized Newtonian fluids.Lecture Notes in Mathematics, 1749, Springer, Berlin-Heidelberg-New York, 2000. Zbl 0964.76003, MR 1810507, 10.1007/BFb0103751 |
| Reference:
|
[FuZha] Fuchs M., Zhang G.: Liouville theorems for entire local minimizers of energies defined on the class $L \log L$ and for entire solutions of the stationary Prandtl-Eyring fluid model.Calc. Var. 44 (2012), no. 1–2, 271–295. MR 2898779, 10.1007/s00526-011-0434-7 |
| Reference:
|
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| Reference:
|
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| Reference:
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[Ga3] Galdi G.: On the existence of symmetric steady-state solutions to the plane exterior Navier-Stokes problem for arbitrary large Reynolds number.Advances in Fluid Dynamics, Quad. Mat., 4, Aracne, Rome, (1999), 1–25. Zbl 0948.35097, MR 1770187 |
| Reference:
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| Reference:
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| Reference:
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