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Stokes system; non-Newtonian fluids; Schauder estimates
The paper is concerned with the solvability theory of the generalized Stokes equations arising in the study of the motion of non-Newtonian fluids.
[1] S. D. Eidelman: Parabolic Systems. Moskva, Nauka, 1964. (Russian) MR 0167726
[2] N. M. Günther: Theory of Potentials. Gostekhizdat, 1947. (Russian)
[3] O. A. Ladyzhenskaya: Mathematical Problems of Viscous Incompressible Flow. Gordon and Breach, 1969. MR 0254401
[4] O. A. Ladyzhenskaya: Attractors for the modifications of the three-dimensional Navier-Stokes equations. Phil. Trans. Roy. Soc. London, ser. A 346 (1994), 173–190. DOI 10.1098/rsta.1994.0017 | MR 1278243 | Zbl 0807.35109
[5] J. Málek, J. Nečas, M. Rokyta, M. Růžička: Weak and Measure-Valued Solutions to Evolution Partial Differential Equations. Chapman and Hall, 1996. MR 1409366
[6] G. A. Seregin: Interior regularity for solutions to the modified Navier-Stokes equations. J. Math. Fluid Mech. 1 (1999), 235–281. DOI 10.1007/s000210050011 | MR 1738752 | Zbl 0961.35106
[7] V. A. Solonnikov: Estimates of solutions of nonstationary linearized Navier-Stokes equations. Trudy Math. Inst. Steklov 70 (1964), 213–317. MR 0171094
[8] V. A. Solonnikov: On the differentiability properties of the solution of the first boundary value problem for nonstationary system of the Navier-Stokes equations. Trudy Mat. Inst. Steklov 73 (1964), 221–291. MR 0172014
[9] V. A. Solonnikov: Estimates of solutions of nonstationary Navier-Stokes equations. Zap. Nauchn. Semin. L.O.M.I. 38 (1973), 153–231. MR 0415097
[10] V. A. Solonnikov: On Green’s matrices for elliptic boundary value problems I. Trudy Mat. Inst. Steklov 110 (1970), 107–145. MR 0289935
[11] V. A. Solonnikov: On the solvability of generalized Stokes equations in the spaces of periodic functions. Preprint No 10, Max-Planck Institut für die Mathematik in den Naturwissenschaften (2000), 1–20. MR 1896933 | Zbl 1037.35060
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