Smoothness of solutions of equations describing generalized Newtonian flows and estimates for the dimensions of their attractors

Izvestiya Mathematics

Volumn 62, Issue 1, 1998, Pages 55-113

  Ladyzhenskaya, O A ^a   Seregin, G A ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

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EID: 33746479000     PISSN: 10645632     EISSN: 14684810     Source Type: Journal    
DOI: 10.1070/IM1998v062n01ABEH000183     Document Type: Article

References (22)

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2. O. A. Ladyzhenskaya, "New equations describing viscous incompressible flows and global solvability of boundary-value problems for them", Trudy Mat. Inst. Steklov. 102 (1967), 85-104;
3. English transl, in Proc. Steklov. Inst. Math. 102 (1970).
4. O. A. Ladyzhenskaya, "Modification of the Navier-Stokes equations for large velocity gradients", Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 7 (1968), 126-154;
5. English transl., Sem. Math., Steklov Math. Inst., Leningrad 7 (1968), 57-69.
6. O. A. Ladyzhenskaya and G. A. Seregin, "On global stability of the two-dimensional visco-plastic flows", Jyväskyllä - St. Petersburg Seminar on PDE's and Numerical Methods, Ber. Univ. Jyväskyllä Math. Inst. 56 (1993), 43-52.
7. O. A. Ladyzhenskaya and G. A. Seregin, "On semigroups generated by initial boundary-value problems describing two-dimensional visco-plastic flows. Non-linear evolution equations", Amer. Math. Soc. Transl., Amer. Math. Soc., Providence Ser. 2, 164 (1995), 99-123.
8. O. A. Ladyzhenskaya, Attractors for semi-groups and evolution equations. Lezioni Lincee, Roma 1988, Cambridge Univ. Press, Cambridge 1991.
9. O. A. Ladyzhenskaya, "The dynamical system generated by the Navier-Stokes equations", Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 27 (1972), 91-114. (Russian)
10. G. A. Seregin, "Flow of the two-dimensional generalized Newtonian fluid", Algebra i Analiz 9:1 (1997), 167-200;
11. English transl., St. Petersburg Math. J. 9 (1998), 121-146.
12. O. A. Ladyzhenskaya, "Supplements and improvements to my publications on attractor theory", Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 182 (1990), 102-112. (Russian)
13. A. Douady and J. Oesterlé, "Dimension de Hausdorff des attracteurs", C. R. Acad. Sci. 290 (1980), 1135-1138.
14. A. V. Babin and M. I. Vishik, "Attractors of partial differential evolution equations and estimates for their dimension", Uspekhi Mat. Nauk 38:4 (1983), 133-187;
15. English transl., Russian Math. Surveys 38:4 (1983), 151-213.
16. O. A. Ladyzhenskaya, "Estimates for the fractal dimension and the number of determining modes for invariant sets of dynamical systems", Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 163 (1987), 105-129;
17. English transl., J. Soviet Math. 49 (1990), 1186-1201.
18. O. A. Ladyzhenskaya, "The solution "in the large" of the boundary-value problem for the Navier-Stokes equations with two spatial variables", Dokl. Akad. Nauk SSSR 123 (1958), 427-429. (Russian)
19. O. A. Ladyzhenskaya, Mathematical problems of the dynamics of a viscous incompressible liquid, Fizmatgiz, Moscow 1951; 2nd edition, Nauka, Moscow 1970; English transl., Gordon and Breach, New York-London 1963.
20. O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and quasi-linear equations of parabolic type, Nauka, Moscow 1967; English transl., American Math. Soc., Providence 1968.
21. O. A. Ladyzhenskaya and N. N. Ural'tseva, Linear and quasi-linear equations of elliptic type, Nauka, Moscow 1973. (Russian)
22. M. Giaquinta, Multiple integrals in the calculus of variations and non-linear elliptic systems, Ann. Math. Studies. No. 105, Princeton University Press, Princeton-New York 1983.