Global weak solutions to inviscid Burgers-Vlasov equations

Huimin Yu; Wentao Cao

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arXiv · 2006.04501

Global weak solutions to inviscid Burgers-Vlasov equations

Huimin Yu·Wentao Cao

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Abstract

In this paper, we consider the existence of global weak solutions to a one dimensional fluid-particles interaction model: inviscid Burgers-Vlasov equations with fluid velocity in $L^\infty$ and particles' probability density in $L^1$. Our weak solution is also an entropy solution to inviscid Burgers' equation. The approach is adding ingeniously artificial viscosity to construct approximate solutions satisfying $L^\infty$ compensated compactness framework and weak $L^1$ compactness framework. It is worthy to be pointed out that the bounds of fluid velocity and the kinetic energy of particles' probability density are both independent of time.

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Huimin Yu, Wentao Cao. 2020-06-08. Global weak solutions to inviscid Burgers-Vlasov equations. https://arxiv.org/abs/2006.04501

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