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arXiv · 1801.08283

Global existence of weak solutions for Navier-Stokes-BGK system

Young-Pil Choi·Seok-Bae Yun
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Abstract

In this paper, we study the global well-posedness of a coupled system of kinetic and fluid equations. More precisely, we establish the global existence of weak solutions for Navier-Stokes-BGK system consisting of the BGK model of Boltzmann equation and incompressible Navier-Stokes equations coupled through a drag forcing term. This is achieved by combining weak compactness of the particle interaction operator based on Dunford-Pettis theorem, strong compactness of macroscopic fields of the kinetic part relied on velocity averaging lemma and a high order moment estimate, and strong compactness of the fluid part by Aubin-Lions lemma.

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Young-Pil Choi, Seok-Bae Yun. 2018-01-25. Global existence of weak solutions for Navier-Stokes-BGK system. https://arxiv.org/abs/1801.08283

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