On a construction of weak solutions to non-stationary Stokes type equations by minimizing variational functionals and their regularity
Commentationes Mathematicae Universitatis Carolinae (2005)
- Volume: 46, Issue: 1, page 161-178
- ISSN: 0010-2628
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top- Gehring F.W., The -integrability of the partial derivatives of a quasiconformal mapping, Acta Math. 130 (1973), 265-277. (1973) MR0402038
- Giaquinta M., Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems, Annals of Mathematics Studies, 105, Princeton University Press, Princeton, NJ, 1983. Zbl0516.49003MR0717034
- Giaquinta M., Giusti E., On the regularity of the minima of variational integrals, Acta Math. 148 (1982), 31-46. (1982) Zbl0494.49031MR0666107
- Giaquinta M., Modica G., Non linear system of the type of the stationary Navier-Stokes system, J. Reine Angew. Math. 330 (1982), 173-214. (1982) MR0641818
- Giaquinta M., Modica G., Regularity results for some classes of higher order non linear elliptic systems, J. Reine Angew. Math. 311/312 (1979), 145-169. (1979) Zbl0409.35015MR0549962
- Giaquinta M., Struwe M., On the partial regularity of weak solutions of non-linear parabolic systems, Math. Z. 179 (1982), 437-451. (1982) MR0652852
- Haga J., Kikuchi N., On the higher integrability for the gradients of the solutions to difference partial differential systems of elliptic-parabolic type, Z. Angew. Math. Phys. 51 (2000), 290-303. (2000) Zbl0969.35134MR1756171
- Hoshino K., Kikuchi N., Gehring theory for time-discrete hyperbolic differential equations, Comment. Math. Univ. Carolinae 39.4 (1998), 697-707. (1998) Zbl1060.35527MR1715459
- Kaplický P., Málek J., Stará J., Global-in-time Hölder continuity of the velocity gradients for fluids with shear-dependent viscosities, Nonlinear Differential Equations Appl. 9 (2002), 175-195. (2002) MR1905824
- Kawabi H., On a construction of weak solutions to non-stationary Navier-Stokes type equations via Rothe's scheme and their regularity, preprint, 2004.
- Kikuchi N., An approach to the construction of Morse flows for variational functionals, Nematics (Orsay, 1990), 195-199, NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 332, Kluwer Acad. Publ., Dordrecht, 1991. Zbl0850.76043MR1178095
- Kikuchi N., A method of constructing Morse flows to variational functionals, Nonlinear World 1 (1994), 131-147. (1994) Zbl0802.35068MR1297075
- Ladyzhenskaya O.A., The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York-London-Paris, 1969. Zbl0184.52603MR0254401
- Nagasawa T., Construction of weak solutions of the Navier-Stokes equations on Riemannian manifold by minimizing variational functionals, Adv. Math. Sci. Appl. 9 (1999), 51-71. (1999) Zbl0944.58021MR1690377
- Naumann J., Wolff M., Interior integral estimates on weak solutions of nonlinear parabolic systems, Institut für Mathematik der Humboldt-Universität zu Berlin, 1994, preprint 94-12.
- Rektorys K., On application of direct variational methods to the solution of parabolic boundary value problems of arbitrary order in the space variables, Czechoslovak Math. J. 21 (1971), 318-339. (1971) Zbl0217.41601MR0298237
- Struwe M., On the Hölder continuity of bounded weak solutions of quasilinear parabolic system, Manuscripta Math. 35 (1981), 125-145. (1981) MR0627929
- Temam R., Navier-Stokes Equations: Theory and Numerical Analysis, North-Holland, Amsterdam, New York, 1977. Zbl0981.35001MR0609732