Regularity results for the quasi-static Bingham variational inequality in dimensions two and three

Mathematische Zeitschrift

Volumn 227, Issue 3, 1998, Pages 525-541

  Fuchs, Martin ^a   Seregin, Gregory ^b  

^a SAARLAND UNIVERSITY   (Germany)

^b STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032371824     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004390     Document Type: Article

References (18)

1. Astarita, G., Marrucci, G., Principles of Non-Newtonian Fluid Mechanics, McGraw-Hill, London, 1974
2. Duvaut, G., Lions, J.L., Inequalities in Mechanics and Physics, Springer Grundlehren Vol.219, Springer Verlag, Berlin, 1976
3. Fuchs, M., On quasi-static non-Newtonian fluids with power law, Preprint No.437, SFB 256 Universität Bonn, Math. Meth. Appl. Sciences 19 (1996), 1225-1232
4. Fuchs, M., Grotowski, J.F., Reuling, J., On variational models for quasistatic Bingham-fluids, Preprint No.412, SFB 256 Universität Bonn; Math. Meth. Appl. Sciences 19 (1996), 991-1015
5. Fuchs, M., Seregin, G.A., Some remarks on non-Newtonian fluids including non-convex perturbations of the Bingham and Powell-Eyring model for viscoplastic fluids, Preprint No.436, SFB 256 Iniversität Bonn, 1995; Math. Models Methods Appl. Sci., Vol. 7, No. 3 (1997), 405-433
6. Galdi, G., An introduction to the mathematical theory of the Navier-Stokes equations, Vol. II, Springer Tracts in Natural Philosophy Vol. 39, Springer Verlag, Berlin, 1994
7. Giaquinta, M., Multiple integrals in the calculus of variations and nonlinear elliptic systems, Princeton University Press Princeton 1983
8. Ionescu, I.R., Sofonea, M., Functional and numerical methods in viscoplasticity, Oxford University Press, Oxford, 1993
9. Ladyzhenskaya, O.A., The mathematical theory of viscous incompressible flow, Gordon and Breach, 1969
10. Ladyzhenskaya, O.A., Seregin, G.A., On semigroups generated by initial-boundary value problems describing two-dimensional visco-plastic flows, Amer.Math.Soc. Transl.(2), 164 (1995), 99-123
11. Ladyzhenskaya, O.A., Solonnikov, V.A., Some problems of vector analysis, and generalized formulations of boundary value problems for the Navier-Stokes equations, Zap.Nauchn.Sem. Leningrad Odtel.Mat. Inst. Steklov (LOMI) 59 (1976), 81-116; English transl. in J. Soviet Math. 10 (1978), No. 2
12. Ladyzhenskaya, O.A., Solonnikov, V.A., Some problems of vector analysis, and generalized formulations of boundary value problems for the Navier-Stokes equations, Zap.Nauchn.Sem. Leningrad Odtel.Mat. Inst. Steklov (LOMI) 59 (1976), 81-116; English transl. in J. Soviet Math. 10 (1978), No. 2
13. Mosolov, P.P., Myasnikov, V.P., Mechanics of rigid plastic media, "Nauka", Moscow, 1981 (Russian)
14. Prager, W., Introduction to the mechanics of continua, Dover Publications, New York, 1973
15. Seregin, G.A., On the differentiability of local extremals of variational problems in the mechanics of rigidly viscoplastic media, Izv. Vyssh. Uchebn. Zaved. Mat. 10 (305), (1987), 23-30; English transi, in Soviet Math. (Iz. VUZ) 31, (1987)
16. Seregin, G.A., On the differentiability of local extremals of variational problems in the mechanics of rigidly viscoplastic media, Izv. Vyssh. Uchebn. Zaved. Mat. 10 (305), (1987), 23-30; English transi, in Soviet Math. (Iz. VUZ) 31, (1987)
17. Seregin, G.A., On differential properties of extremals of variational problems of the mechanics of viscoplastic media, Proc. Steklov Inst. Math. 3 (1991), 147-157
18. Seregin, G.A., Continuity for the strain velocity tensor in two-dimensional variational problems from the theory of the Bingham fluid, Preprint no. 402, SFB 256 Universität Bonn 1995