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On a Resolvent Estimate of the Stokes Equation on an Infinite Layer Part 2, λ=: 0 Case

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Abstract.

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 λ is close to zero (see eq.(1.1)). Combining this result with that in [1], 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.

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Authors and Affiliations

  1. Department of Mathematical Sciences, School of Science and Engineering, Waseda University, Ohkubo 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan. E-mail: abe@ruri.waseda.jp, , , , , , JP

    T. Abe

  2. Advanced Research Institute for Science and Engineering, Waseda University, Department of Mathematical Sciences, School of Science and Engineering, Waseda University, Ohkubo 3-4-1, Shinjuku-ku, Tokyo 169-8555, Japan. E-mail: yshibata@waseda.jp , , , , , , JP

    Y. Shibata

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  1. T. Abe
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  2. Y. Shibata
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Accepted: June 10, 2002

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Abe, T., Shibata, Y. On a Resolvent Estimate of the Stokes Equation on an Infinite Layer Part 2, λ=: 0 Case. J. math. fluid mech. 5, 245–274 (2003). https://doi.org/10.1007/s00021-003-0075-5

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  • DOI: https://doi.org/10.1007/s00021-003-0075-5

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