Article
Keywords:
Stokes system; non-Newtonian fluids; Schauder estimates
Summary:
The paper is concerned with the solvability theory of the generalized Stokes equations arising in the study of the motion of non-Newtonian fluids.
References:
[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
[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
[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