<p>We study the homogenization of stochastic convective Brinkman-Forchheimer equations (SCBFE) or the tamed Navier-Stokes equations which describe the motion of incompressible fluid flows in satured porous medium. We combine some compactness arguments such as Prokhorov’s and Skorokhod’s probabilistic compactness results with the sigma-convergence method to prove that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized stochastic problem with constant coefficients.</p>

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Homogenization of stochastic convective Brinkman-Forchheimer equations

  • Aurelien Fouetio

摘要

We study the homogenization of stochastic convective Brinkman-Forchheimer equations (SCBFE) or the tamed Navier-Stokes equations which describe the motion of incompressible fluid flows in satured porous medium. We combine some compactness arguments such as Prokhorov’s and Skorokhod’s probabilistic compactness results with the sigma-convergence method to prove that the sequence of solutions of the original problem converges in suitable topologies to the solution of a homogenized stochastic problem with constant coefficients.