Regularity for stokes and generalized stokes systems under nonhomogeneous slip-type boundary conditions

Advances in Differential Equations

Volumn 9, Issue 9-10, 2004, Pages 1079-1114

  Beirao da Veiga H ^a  

^a UNIVERSITY OF PISA   (Italy)

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EID: 12144261419     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (45)

1. S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math., 17 (1964), 35-92.
2. G.J. Beavers and D.D. Joseph, Boundary conditions of a naturally permeable wall, J. Fluid Mech., 30 (1967), 197-207.
3. C. Bègue, C. Conca, F. Murat, and O. Pironeau, Leséquations 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, 169-264.
4. 2-regularity theorems for linear nonhomogeneous Stokes systems, Portugaliae Mathematica, 54 (1997), 271-286.
5. H. Beirão da Veiga, On the existence of strong solutions to a coupled fluid-structure evolution problem, J. Math. Fluid Mechanics, 6 (2004), 21-52.
6. +, Math. Annalen, to appear.
7. H. Beirão da Veiga, On the regularity of flows with Ladyzhenskaya shear dependent viscosity and slip or non-slip boundary conditions, Comm. Pure Appl. Math., 57 (2004), 1-26.
8. H. Beirão da Veiga, On the regularity of flows with Ladyzhenskaya shear dependent viscosity and slip or non-slip boundary conditions. Part II: The evolution problem, to appear.
9. J. Bemelmans, Gleichgewichtfiguren zäher Flüssigkeiten mit Oberflächenspannung, Analysis, 1 (1981), 241-282.
10. J. Bourgain and H. Brezis, On the equation div Y = f on Td, J. Amer. Math. Soc., 16 (2003), 393-426.
11. L. Cattabriga, Su un problema al contorno relativo al sistema di equazioni di Stokes, Rend. Sem. Mat. Univ. Padova, 17 (1964), 308-340.
12. C. Conca, On the application of the homogenization theory to a class of problems arising in fluid mechanics, J. Math. Pures Appl., 64 (1985), 31-75.
13. P. Constantin and C. Foias, "Navier-Stokes Equations," The University of Chicago Press, Chicago, 1988.
14. G. Duvaut and J.L. Lions, "Inequalities in Mechanics and Physics," Springer Verlag, Heidelberg, 1976.
15. A.V. Fursikov, M.D. Gunzburger, and L.S. Hou, Boundary value problems and optimal boundary control for the Navier-Stokes system: the two dimensional case, SIAM J. Control and Optim., 36 (1998), 852-894.
16. A.V. Fursikov, M.D. Gunzburger, and L.S. Hou, Trace theorems for three-dimensional, time-dependent solenoidal vector fields and their applications, Trans. Amer. Math. Soc., 354 (2002), 1079-1116.
17. G.P. Galdi, C.G. Simader, and H. Sohr, On the Stokes problem in Lipschitz domains, Ann. Mat. Pura Appl., 167 (1994), 147-163.
18. G.P. Galdi, "An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Linearized Steady Problems," Springer Tracts in Natural Philosophy, 38, Second corrected printing, Springer-Verlag, 1998.
19. G.P. Galdi and W. Layton, Approximation of the larger eddies in fluid motion: A model for space filtered flow, Math. Models and Meth. in Appl. Sciences, 3 (2000), 343-350.
20. Y. Giga, Analicity of the semigroup generated by the Stokes operator in Lr-spaces, Math. Z., 178 (1981), 287-329.
21. V. Girault and P.-A. Raviart, "Finite Element Approximation of the Navier-Stokes Equations," Lecture Notes in Mathematics, 749, Springer Verlag, Berlin-Heidelberg, 1979.
22. C. Grandmont and Y. Maday, Fluid-structure interaction: A theoretical point of view, Revue Europèenne Elem. Finis, to appear.
23. V. John, 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.
24. V. John, "Large Eddy Simulation of Turbulent Incompressible Flows. Analytical and Numerical Results for a Class of LES Models," Habilitationsschrift, Otto-von- Guericke-Universität Magdeburg, April 2002.
25. S.G. Krein and G.I. Laptev, On the problem of the motion of a viscous fluid in an open vessel, Functional Anal. Appl., 2 (1968), 38-47.
26. O.A. Ladysenskaya, "The Mathematical Theory of Viscous Incompressible Flow," Gordon and Breach, New York, 1969.
27. 2 , St. Petersburg Math. J., 13 (2002), 601-612.
28. A. Liakos, Discretization of the Navier-Stokes equations with slip boundary condition, Num. Meth. for Partial Diff. Eq., 1 (2001), 1-18.
29. J.-L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires," Dunod, Paris, 1969.
30. V.G. Mazja, B.A. Plamenevskii, and L.T. Stupyalis, The three-dimensional problem of steady-state motion of a fluid with a free surface, Trans. Am. Math. Soc., 123 (1984), 171-268.
31. J. Nečas, "Les Methodes Directes en Theorie des Equations Elliptiques," Academia, Prague, 1967.
32. L. Nirenberg, On elliptic partial differential equations, An. Sc. Norm. Sup. Pisa, 13 (1959), 116-162.
33. C. Pare's, Existence, uniquiness and regularity of solutions of the equations of a turbulence model for incompressible fluids, Appl. Analysis, 43 (1992), 245-296.
34. H. Saito and L.E. Scriven, Study of the coating flow by the finite element method, J. Comput. Phys., 42 (1981), 53-76.
35. J. Serrin, Mathematical principles of classical fluid nechanics, in "Encyclopedia of Physics," VIII, pp. 125-263, Springer-Verlag, Berlin, 1959.
36. J. Silliman and L.E. Scriven, Separating flow near a staic contact line: slip at a wall and shape of a free surface, J. Comput. Physics, 34 (1980), 287-313.
37. V.A. Solonnikov, On estimates of Green tensors for certain boundary value problems, Dokl. Akad. Nauk. SSSR, 29 (1960), 988-991.
38. V.A. Solonnikov, 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.
39. V.A. Solonnikov, Solvability of three dimensional problems with a free boundary for a stationary system of Navier-Stokes equations, J. Sov. Math., 21 (1983), 427-450.
40. p-estimates for solutions to the initial-boundary-value problem for the generalized Stokes equations in a half-space, Probl. Mat. Anal., 20 (2000), 243-270. English translation: J. Sci. (New York), 102 (2000), no. 5, 4523-4543.
41. p-estimates for solutions to the initial boundary-value problem for the generalized Stokes system in a bounded domain, Probl. Mat. Anal., 21 (2000), 211-263. English translation: J. Math. Sci. (New York), 105 (2001), no. 5.
42. V.A. Solonnikov and V.E. Ščadilov, On a boundary value problem for a stationary system of Navier-Stokes equations, Proc. Steklov Inst. Math., 125 (1973), 186-199.
43. L. Tartar, Nonlinear partial differential equations using compactness method, University of Wisconsin-Madison and Mathematics Research Center Technical Summary Report no. 1584, February 1976.
44. R. Temam, "Navier-Stokes Equations," North-Holland, Amsterdam, 1984.
45. R. Verfürth, Finite element approximation of incompressible Navier-Stokes equations with slip boundary conditions, Numer. Math., 50 (1987), 697-721.