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On a construction of weak solutions to non-stationary Stokes type equations by minimizing variational functionals and their regularity. (English) Zbl 1121.35100
Non-stationary Stokes type equations with bounded measurable coefficients in the second order differential terms are studied and the regularity of weak solutions in the sense of Gehring-Giaquinta-Modica is proved. To construct weak solutions, the author uses a semi-discretization in time variable of gradient flows (Morse flows) of the corresponding functional. This is in fact the Rothe’s method taking into consideration the variational structure of the problem. A higher integrability of gradients is proved for approximate weak solutions and then also for the solution of the original problem. The local estimates obtained for gradients are independent of approximation.
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
35J50 Variational methods for elliptic systems
39A12 Discrete version of topics in analysis
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