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Global existence and large time behaviour of solutions for the Vlasov-Stokes equations

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Abstract

One considers the Vlasov-Stokes equations to model the motion of a solid particles suspension in a Stokes flow. The dispersed phase, is modelled by a transport kinetic equation with acceleration corresponding to the Stokes drag and gravity field. The viscous fluid is assumed to be incompressible and its velocity satisfies the Stokes equations with an external force. This force is due to the relative velocity of the dispersed phase in the fluid. Denoting byN the space dimension, we prove global existence results of solutions forN ≥ 2. We also obtain the large time asymptotic behaviour of the solutions forN = 2 andN = 3.

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Author notes

  1. K. Hamdache

    Present address: Institut Galilée. Laga, CNRS, Université de Paris Novol, Avenue J. B. Clément, F-93430, Villetaneuse, France

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  1. CNRS-Université de Bordeaux I, M.A., 351, Cours de la Libération, F-33405, Talence cedex, France

    K. Hamdache

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Hamdache, K. Global existence and large time behaviour of solutions for the Vlasov-Stokes equations. Japan J. Indust. Appl. Math. 15, 51–74 (1998). https://doi.org/10.1007/BF03167396

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  • DOI: https://doi.org/10.1007/BF03167396

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