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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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