Title:
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On existence and regularity of solutions to a class of generalized stationary Stokes problem (English) |
Author:
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Huy, Nguyen Duc |
Author:
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Stará, Jana |
Language:
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English |
Journal:
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Commentationes Mathematicae Universitatis Carolinae |
ISSN:
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0010-2628 (print) |
ISSN:
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1213-7243 (online) |
Volume:
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47 |
Issue:
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2 |
Year:
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2006 |
Pages:
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241-264 |
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Category:
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math |
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Summary:
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We investigate the existence of weak solutions and their smoothness properties for a generalized Stokes problem. The generalization is twofold: the Laplace operator is replaced by a general second order linear elliptic operator in divergence form and the ``pressure'' gradient $\nabla p$ is replaced by a linear operator of first order. (English) |
Keyword:
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generalized Stokes problem |
Keyword:
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weak solutions |
Keyword:
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regularity up to the boundary |
MSC:
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35B65 |
MSC:
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35D05 |
MSC:
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35D10 |
MSC:
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35J55 |
MSC:
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35Q30 |
MSC:
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35Q35 |
MSC:
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76D03 |
MSC:
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76D07 |
idZBL:
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Zbl 1150.76010 |
idMR:
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MR2241530 |
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Date available:
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2009-05-05T16:57:04Z |
Last updated:
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2012-04-30 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/119590 |
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Reference:
|
[1] Adams R.A.: Sobolev Spaces.Academic Press, New York, 1975. Zbl 1098.46001, MR 0450957 |
Reference:
|
[2] Agmon S., Douglis A., Nirenberg L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I.Comm. Pure Appl. Math. 12 (1959), 623-727. Zbl 0093.10401, MR 0125307 |
Reference:
|
[3] Agmon S., Douglis A., Nirenberg L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II.Comm. Pure Appl. Math. 17 (1964), 35-92. Zbl 0123.28706, MR 0162050 |
Reference:
|
[4] Amrouche C., Girault V.: Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension.Czechoslovak Math. J. 44(119) (1994), 1 109-140. Zbl 0823.35140, MR 1257940 |
Reference:
|
[5] Fuchs M., Seregin G.: Variational methods for problems from plasticity theory and for generalized Newtonian fluids.Lecture Notes in Mathematics, 1749, Springer Verlag, Berlin, 2000. Zbl 0964.76003, MR 1810507 |
Reference:
|
[6] Galdi G.P.: An Introduction to the Mathematical Theory of the Navier-Stokes Equations, I: Linearized Steady Problems.Springer Verlag, New York, 1994. MR 1284205 |
Reference:
|
[7] Nečas J.: Les méthodes directes en théorie des équations elliptiques.Academia, Prague, 1967. MR 0227584 |
Reference:
|
[8] Sohr H.: The Navier-Stokes Equations. An Elementary Functional Analytic Approach.Birkhäuser Verlag, Basel, 2001. Zbl 0983.35004, MR 1928881 |
Reference:
|
[9] Solonnikov V.A.: Initial-boundary value problem for generalized Stokes equations.Math. Bohem. 126 (2001), 2 505-519. Zbl 1003.76016, MR 1844287 |
Reference:
|
[10] Stará J.: Regularity results for non-linear elliptic systems in two dimensions.Ann. Scuola Norm. Sup. Pisa (3) 25 (1971), 163-190. MR 0299935 |
Reference:
|
[11] Hron J., Málek J., Nečas J., Rajagopal K.R.: Numerical simulations and global existence of solutions of two-dimensional flows of fluids with pressure- and shear-dependent viscosities.Math. Comput. Simulation 61 3-6 (2003), 297-315. Zbl 1205.76159, MR 1984133 |
Reference:
|
[12] Málek J., Nečas J., Rajagopal K.R.: Global analysis of the flows of fluids with pressure-dependent viscosities.Arch. Ration. Mech. Anal. 165 (2002), 243-269. Zbl 1022.76011, MR 1941479 |
Reference:
|
[13] Franta M., Málek J., Rajagopal K.R.: On steady flows of fluids with pressure- and shear-dependent viscosities.Proc. Royal Soc. London Ser. A 461 (2005), 651-670. Zbl 1145.76311, MR 2121929 |
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