Regularity of solutions to a non homogeneous boundary value problem for general Stokes systems in R+n

Mathematische Annalen

Volumn 331, Issue 1, 2005, Pages 203-217

  Da Veiga, H Beirão ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 12144276609     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00208-004-0578-2     Document Type: Article

References (36)

1. 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, 35-92 (1964)
2. Avantaggiati, A.: Spazi di Sobolev con peso ed alcune applicazioni. Bolletino UMI 13-A, 1-52 (1976)
3. Beavers, G.J., Joseph, D.D.: Boundary conditions of a naturally permeable wall. Bolletino U.M.I. serie 5 13-A, 1-52 (1976)
4. Bègue, C., Conca, C., Murat, F., Pironeau, O.: Les équations de Stokes et de Navier-Stokes avec des conditions aux limites sur la pression. Collège de France Seminar-Vol.IX, 1988, Pitman Research Notes in Mathematics Series 181, pp. 169-264
5. Beirão da Veiga, H.: Regularity for Stokes and generalized Stokes systems under nonhomogeneous slip type boundary conditions. Advances Diff. Eq. 9, 1079-1114 (2004)
6. Beirão da Veiga, H.: On the regularity of flows with Ladyzhenskaya shear dependent viscosity and slip or non-slip boundaiy conditions. Comm. Pure Appl. Math. 57, 1-26 (2004)
7. Bemelmans, J.: Gleichgewichtfiguren zaher Flussigkeiten mit Oberflachenspannung. Anal. 1, 241-282 (1981)
8. Cattabriga, L.: Su un problema al contorno relative al sistema di equazioni di Stokes. Rend. Sem. Mat. Univ. Padova 17, 308-340 (1964)
9. Conca, C.: On the application of the homogenization theory to a class of problems arising in fluid mechanics. J. Math. Pures Appl. 64, 31-75 (1985)
10. Constantin, P., Foias, C.: Navier-Stokes Equations. The University of Chicago Press, Chicago, 1988
11. Duvaut, G., Lions, J.L.: Inequalities in Mechanics and Physics. Springer Verlag, Heidelberg, 1976
12. Galdi, G.P., Simader, C.G., Sohr, H.: On the Stokes problem in Lipschitz domains. Ann. Mat. Pura Appl. 167, 147-163 (1994)
13. Galdi, G.P.: An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Vol. I: Linearized Steady Problems. Springer Tracts in Natural Philosophy, Springer-Verlag, 38, 1998
14. Galdi, G.P., Layton, W.: Approximation of the larger eddies in fluid motion II: A model for space filtered flow. Math. Models Meth. Appl. Sci. 3, 343-350 (2000)
15. r-spaces. Math. Z. 178, 287-329 (1981)
16. Hanouzet, B.: Espaces de Sobolev avec poids. Application au problème de Dirichlet dans un demi espace. Rend. Sem. Mat. Univ. Padova 46, 227-272 (1971)
17. John, V.: Slip with friction and penetration with resistence boundary conditions for the Navier-Stokes equations-numerical tests and aspects of the implementations. J. Comp. Appl. Math., to appear
18. Krein, S.G., Laptev, G.I.: On the problem of the motion of a viscous fluid in an open vessel. Functional Anal. Appl. 2, 38-47 (1968)
19. Ladyzenskaya, O.A.: The Mathematical Theory of Viscous Incompressible Flow. Gordon and Breach, New-York, 1969
20. (-1). St. Petersburg Math. J. 13, 601-612 (2002)
21. Liakos, A.: Discretization of the Navier-Stokes equations with slip boundary condition. Num. Meth. Partial Diff. Eq. 1, 1-18 (2001)
22. Lions, J.-L.: Problèmes aux Limites dans les Équations aux Dérivées Partielles. Presses de l'Université de Montréal, Montréal, 1965
23. Lions, J.-L.: Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod, Paris, 1969
24. Mazja, V.G., Plamenevskii, B.A., Stupyalis, L.T.: The three-dimensional problem of stedy-state motion of a fluid with a free surface. Trans. Am. Math. Soc. 123, 171-268 (1984)
25. Nečas, J.: Les Methodes Directes en Theorie des Equations Elliptiques. Academia, Prague, 1967
26. Nirenberg, L.: On elliptic partial differential equations. An. Sc. Norm. Sup. Pisa 13, 116-162 (1959)
27. Parés, C.: Existence, uniqueness and regularity of solutions of the equations of a turbulence model for incompressible fluids. Appl. Anal. 43, 245-296 (1992)
28. Saito, H., Scriven, L.E.: Study of the coating flow by the finite elemente method. J. Comput. Phys. 42, 53-76 (1981)
29. Silliman, J., Scriven, L.E.: Separating flow near a staic contact line: slip at a wall and shape of a free surface. J. Comput. Phys. 34, 287-313 (1980)
30. Solonnikov, V.A.: On estimates of Green tensors for certain boundary value problems. Dokl. Akad. Nauk. SSSR 29, 988-991 (1960)
31. Solonnikov, V.A.: General boundary value problems for Douglis-Nirenberg elliptic systems.II. Proceedings of the Steklov Institute of Mathematics. 92, 1966; English translation, American Mathematical Society, 1968
32. Solonnikov, V.A.: Solvability of three dimensional problems with a free boundary for a stationary system of Navier-Stokes equations. J. Sov. Math. 21, 427-450 (1983)
33. Solonnikov, V.A., Ščadilov, V.E.: On a boundary value problem for a stationary system of Navier-Stokes equations. Proc. SteklovInst. Math. 125, 186-199 (1973)
34. Tartar, L.: Nonlinear partial differential equations using compactness method. University of Wisconsin-Madison and Mathematics Research Center Technical Summary Report 1584, Feebruary 1976
35. Temam, R.: Navier-Stokes Equations. North-Holland, Amsterdam, 1984
36. Verfurth, R.: Finite element approximation of incompressible Navier-Stokes equations with slip boundary conditions. Numer. Math. 50, 697-721 (1987)