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On a resolvent estimate of the Stokes equation on an infinite layer. II: \( \lambda=0\) case. (English) Zbl 1162.76328
Summary: This paper is concerned with the standard \(L_p\) estimate of solutions to the Stokes resolvent problem on an infinite layer in the case where \(\lambda\) is close to zero (see eq.(1.1)). Combining this result with that in [T. Abe, Y. Shibata, J. Math. Soc. Japan 55, No. 2, 469–497 (2003; Zbl 1048.35052)], we find that the Stokes operator on an infinite layer generates an analytic semigroup. As an application, we prove the local stability of some steady flows.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
35B45 A priori estimates in context of PDEs
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