STRONG CONVERGENCE OF A VECTOR-BGK MODEL TO THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS VIA THE RELATIVE ENTROPY METHOD - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal de Mathématiques Pures et Appliquées Année : 2019

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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hal-01846266 , version 1 (21-07-2018)

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Roberta Bianchini. STRONG CONVERGENCE OF A VECTOR-BGK MODEL TO THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS VIA THE RELATIVE ENTROPY METHOD. Journal de Mathématiques Pures et Appliquées, 2019, 132, pp.280-307. ⟨10.1016/j.matpur.2019.04.004⟩. ⟨hal-01846266⟩
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