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The Initial Value Problem for the Navier-Stokes Equations with General Slip Boundary Condition in Hölder Spaces

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Abstract.

The initial-boundary value problem for the Navier-Stokes equations including the slipping on the solid boundary is considered. The unique solvability is established in Hölder spaces locally in time for the three-dimensional problem and globally in time for the two-dimensional problem without so-called smallness restrictions.

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Authors and Affiliations

  1. Hirosaki University, Department of Mathematics, Hirosaki 036-8560, Japan. E-mail: sitoh@cc.hirosaki-u.ac.jp, , , , , , JP

    S. Itoh

  2. Fukuoka University, Department of Applied Mathematics, Fukuoka 814-0180, Japan. E-mail: naoto@cis.fukuoka-u.ac.jp, , , , , , JP

    N. Tanaka

  3. Keio University, Department of Mathematics, Yokohama 223-8522, Japan. E-mail: tani@math.keio.ac.jp, , , , , , JP

    A. Tani

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  1. S. Itoh
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  2. N. Tanaka
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  3. A. Tani
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Accepted: June 14, 2002

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Itoh, S., Tanaka, N. & Tani, A. The Initial Value Problem for the Navier-Stokes Equations with General Slip Boundary Condition in Hölder Spaces. J. math. fluid mech. 5, 275–301 (2003). https://doi.org/10.1007/s00021-003-0074-6

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  • DOI: https://doi.org/10.1007/s00021-003-0074-6

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