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Long-Time Behavior for the Two-Dimensional Motion of a Disk in a Viscous Fluid

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Abstract

In this article, we study the long-time behavior of solutions of the two-dimensional fluid-rigid disk problem. The motion of the fluid is modeled by the two-dimensional Navier–Stokes equations, and the disk moves under the influence of the forces exerted by the viscous fluid. We first derive L p−L q decay estimates for the linearized equations and compute the first term in the asymptotic expansion of the solutions of the linearized equations. We then apply these computations to derive time-decay estimates for the solutions to the full Navier–Stokes fluid-rigid disk system.

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Authors and Affiliations

  1. Institut de Mathématiques de Toulouse; UMR 5219, Université de Toulouse; CNRS; UPS IMT, 31062, Toulouse Cedex 9, France

    S. Ervedoza

  2. Université Paris-Dauphine, CEREMADE, UMR 7534, CNRS, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    M. Hillairet

  3. Université Paris-Diderot (Paris 7), Institut de Mathématiques de Jussieu, Paris Rive Gauche, UMR 7586, CNRS, Bâtiment Sophie Germain, Case 7012, 75205, Paris Cedex 13, France

    C. Lacave

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  1. S. Ervedoza
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  2. M. Hillairet
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  3. C. Lacave
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Correspondence to C. Lacave.

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Communicated by L. Caffarelli

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Ervedoza, S., Hillairet, M. & Lacave, C. Long-Time Behavior for the Two-Dimensional Motion of a Disk in a Viscous Fluid. Commun. Math. Phys. 329, 325–382 (2014). https://doi.org/10.1007/s00220-014-1884-5

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  • DOI: https://doi.org/10.1007/s00220-014-1884-5

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