Estimates of solutions of the Stokes equations in S. L. Sobolev spaces with a mixed norm. (English. Russian original) Zbl 1068.35093
J. Math. Sci., New York 123, No. 6, 4637-4653 (2004); translation from Zap. Nauchn. Semin. POMI 288, 204-231 (2002).
Summary: Estimates of solutions of the evolutionary Stokes and Navier-Stokes equations in a bounded \(n\)-dimensional domain are obtained. By using explicit formulas, the structure of these solutions is analyzed in the case of a half-space.
MSC:
| 35Q30 | Navier-Stokes equations |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
| 35C15 | Integral representations of solutions to PDEs |
| 76D07 | Stokes and related (Oseen, etc.) flows |
