Stokes and Navier–Stokes problems in a half-space: the existence and uniqueness of solutions a priori nonconvergent to a limit at infinity
✍ Scribed by P. Maremonti
- Publisher
- Springer US
- Year
- 2009
- Tongue
- English
- Weight
- 670 KB
- Volume
- 159
- Category
- Article
- ISSN
- 1573-8795
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📜 SIMILAR VOLUMES
We shall construct a periodic strong solution of the Navier-Stokes equations for some periodic external force in a perturbed half-space and an aperture domain of the dimension n¿3. Our proof is based on L p -L q estimates of the Stokes semigroup. We apply L p -L q estimates to the integral equation
We construct a class of weak solutions to the Navier᎐Stokes equations, which have second order spatial derivatives and one order time derivatives, of p power s Ž 2, r Ž .. summability for 1p F 5r4. Meanwhile, we show that u g L 0, T ; W ⍀ with 1rs q 3r2 r s 2 for 1r F 5r4. r can be relaxed not to ex
## Abstract In this paper we consider a resolvent problem of the Stokes operator with some boundary condition in the half space, which is obtained as a model problem arising in evolution free boundary problems for viscous, incompressible fluid flow. We show standard resolvent estimates in the __L~q