Asymptotic analysis of Vlasov-type equations under strong local alignment regime

2014/12/09 by Moon-Jin Kang, Alexis Vasseur, Kang, Moon-Jin +1 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Mathematical Biology Tumor Growth

paper · pdf · doi:10.48550/arxiv.1412.3119

openalex publication_date 2014/12/09 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/01

Abstract

We consider the hydrodynamic limit of a collisionless and non-diffusive kinetic equation under strong local alignment regime. The local alignment is first considered by Karper, Mellet and Trivisa in [24], as a singular limit of an alignment force proposed by Motsch and Tadmor in [32]. As the local alignment strongly dominate, a weak solution to the kinetic equation under consideration converges to the local equilibrium, which has the form of mono-kinetic distribution. We use the relative entropy method and weak compactness to rigorously justify the weak convergence of our kinetic equation to the pressureless Euler system.

Citations

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Cited by

• Hydrodynamic limit for compressible Navier-Stokes-Vlasov-Poisson equations with local alignment force
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