×

zbMATH — the first resource for mathematics

On a resolvent estimate of the Stokes equation on an infinite layer. (English) Zbl 1048.35052
The authors establish the weak solvability of the title problem, and prove standard \(L_p\) estimates for the solution. The proof is based on a partial Fourier transform which reduces the original problem to a two-point boundary value problem for a system of ordinary differential equations with parameter. Then an application of Agmon-Douglis-Nirenberg type estimates of singular integrals provides the desired result.

MSC:
35Q30 Navier-Stokes equations
76D07 Stokes and related (Oseen, etc.) flows
PDF BibTeX XML Cite
Full Text: DOI