| Title:
|
On a construction of weak solutions to non-stationary Stokes type equations by minimizing variational functionals and their regularity (English) |
| Author:
|
Kawabi, Hiroshi |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
161-178 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we prove that the regularity property, in the sense of Gehring-Giaquinta-Modica, holds for weak solutions to non-stationary Stokes type equations. For the construction of solutions, Rothe's scheme is adopted by way of introducing variational functionals and of making use of their minimizers. Local estimates are carried out for time-discrete approximate solutions to achieve the higher integrability. These estimates for gradients do not depend on approximation. (English) |
| Keyword:
|
non-stationary Stokes type equations |
| Keyword:
|
higher integrability of gradients |
| Keyword:
|
Caccioppoli type estimate |
| Keyword:
|
Gehring theory |
| Keyword:
|
Rothe's scheme |
| MSC:
|
35J50 |
| MSC:
|
35Q30 |
| MSC:
|
39A12 |
| MSC:
|
47J30 |
| MSC:
|
49S05 |
| MSC:
|
76D03 |
| MSC:
|
76D05 |
| MSC:
|
76D07 |
| MSC:
|
76M30 |
| idZBL:
|
Zbl 1121.35100 |
| idMR:
|
MR2175868 |
| . |
| Date available:
|
2009-05-05T16:50:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119517 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Giaquinta M., Giusti E.: On the regularity of the minima of variational integrals.Acta Math. 148 (1982), 31-46. Zbl 0494.49031, MR 0666107 |
| Reference:
|
[4] Giaquinta M., Modica G.: Non linear system of the type of the stationary Navier-Stokes system.J. Reine Angew. Math. 330 (1982), 173-214. MR 0641818 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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[8] Hoshino K., Kikuchi N.: Gehring theory for time-discrete hyperbolic differential equations.Comment. Math. Univ. Carolinae 39.4 (1998), 697-707. Zbl 1060.35527, MR 1715459 |
| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
