| Title:
|
Initial-boundary value problem for generalized Stokes equations (English) |
| Author:
|
Solonnikov, V. A. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
505-519 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Stokes system |
| Keyword:
|
non-Newtonian fluids |
| Keyword:
|
Schauder estimates |
| MSC:
|
35B45 |
| MSC:
|
35Q30 |
| MSC:
|
76A05 |
| MSC:
|
76D03 |
| idZBL:
|
Zbl 0981.35047 |
| idMR:
|
MR1844287 |
| DOI:
|
10.21136/MB.2001.134018 |
| . |
| Date available:
|
2009-09-24T21:53:23Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134018 |
| . |
| Reference:
|
[1] S. D. Eidelman: Parabolic Systems.Moskva, Nauka, 1964. (Russian) MR 0167726 |
| Reference:
|
[2] N. M. Günther: Theory of Potentials.Gostekhizdat, 1947. (Russian) |
| Reference:
|
[3] O. A. Ladyzhenskaya: Mathematical Problems of Viscous Incompressible Flow.Gordon and Breach, 1969. MR 0254401 |
| Reference:
|
[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. Zbl 0807.35109, MR 1278243, 10.1098/rsta.1994.0017 |
| Reference:
|
[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 |
| Reference:
|
[6] G. A. Seregin: Interior regularity for solutions to the modified Navier-Stokes equations.J. Math. Fluid Mech. 1 (1999), 235–281. Zbl 0961.35106, MR 1738752, 10.1007/s000210050011 |
| Reference:
|
[7] V. A. Solonnikov: Estimates of solutions of nonstationary linearized Navier-Stokes equations.Trudy Math. Inst. Steklov 70 (1964), 213–317. MR 0171094 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[10] V. A. Solonnikov: On Green’s matrices for elliptic boundary value problems I.Trudy Mat. Inst. Steklov 110 (1970), 107–145. MR 0289935 |
| Reference:
|
[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. Zbl 1037.35060, MR 1896933 |
| . |
