Strong convergence of a vector-BGK model to the incompressible Navier-Stokes equations via the relative entropy method

Roberta Bianchini

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arXiv · 1807.04044

Strong convergence of a vector-BGK model to the incompressible Navier-Stokes equations via the relative entropy method

Roberta Bianchini

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Abstract

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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Roberta Bianchini. 2018-07-11. Strong convergence of a vector-BGK model to the incompressible Navier-Stokes equations via the relative entropy method. https://arxiv.org/abs/1807.04044

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