STRONG CONVERGENCE OF A VECTOR-BGK MODEL TO THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS VIA THE RELATIVE ENTROPY METHOD
Résumé
The aim of this paper is to prove the strong convergence of the solutions to a vector-BGK model under the diffusive scaling to the incompressible Navier-Stokes equations on the two-dimensional torus. This result holds in any interval of time [0, T ], with T > 0. We also provide the global in time uniform boundedness of the solutions to the approximating system. Our argument is based on the use of local in time H^s-estimates for the model, established in a previous work, combined with the L^2-relative entropy estimate and the interpolation properties of the Sobolev spaces.
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