On a resolvent estimate of the Stokes system in a half space arising from a free boundary problem for the Navier–Stokes equations |
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| Authors: | Y. Shibata S. Shimizu |
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| Affiliation: | 1. Department of Mathematics, School of Science and Engineering, Waseda University, Ohkubo 3‐4‐1, Shinjuku‐ku, Tokyo 169‐8555, Japan;2. Faculty of Science, Shizuoka University, Shizuoka 422‐8529, Japan;3. Phone: +81 54 238 4718, Fax: +81 54 238 4718 |
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| 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 Lq framework (1 < q < ∞), applying some kernel estimates to concrete solution formulas. The Volevich trick in [21] plays a fundamental role in estimating solutions (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Resolvent estimate Lq framework free boundary problem Stokes equation surface tension gravity force |
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