Hydrodynamic limit for the inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck equations

Su, Yunfei; Yao, Lihua

doi:10.1016/j.jde.2019.12.027

Cited by 7 publications

(2 citation statements)

References 23 publications

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“…The second one requires the use of relative entropy methods. These results have also been extended by Mellet and Vasseur in [68] for a compressible Navier-Stokes system and by Su and Yao in [73] for a non-homogeneous system.…”

Section: Broad Panorama On Hydrodynamic Limits For Fluid-kinetic Systemsmentioning

confidence: 56%

Global derivation of a Boussinesq-Navier-Stokes type system from fluid-kinetic equations

Ertzbischoff¹

2022

Preprint

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We study a hydrodynamic limit of the Vlasov-Navier-Stokes system with external gravity force, following the framework introduced by Han-Kwan and Michel in [44]. We answer a question raised in the latter concerning the derivation of a Boussinesq-Navier-Stokes type system for arbitrarily large times, starting from the previous fluid-kinetic system. To do so, we consider a particular spatial geometric setting corresponding to the half-space case. Our proof is based on an absorption effect at the boundary which leads to crucial decay in time estimates. Contents

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Section: Broad Panorama On Hydrodynamic Limits For Fluid-kinetic Systemsmentioning

confidence: 56%

Global derivation of a Boussinesq-Navier-Stokes type system from fluid-kinetic equations

Ertzbischoff¹

2022

Preprint

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“…Lucas Philip and Bernie D. Shizgal [13] consider the one-dimensional bistable Fokker-Planck equation with specific drift and diffusion coefficients so as to model protein folding. Yunfei Su and Lei Yao [14] study the hydrodynamic limit for the inhomogeneous incompressible Fokker-Planck equations.…”

Section: Introductionmentioning

confidence: 99%

The asymptotic solution of a singularly perturbed Cauchy problem for Fokker-Planck equation

Bouatta

Vasilyev

Vinitsky

2021

Discrete and Continuous Models

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The asymptotic method is a very attractive area of applied mathematics. There are many modern research directions which use a small parameter such as statistical mechanics, chemical reaction theory and so on. The application of the Fokker-Planck equation (FPE) with a small parameter is the most popular because this equation is the parabolic partial differential equations and the solutions of FPE give the probability density function. In this paper we investigate the singularly perturbed Cauchy problem for symmetric linear system of parabolic partial differential equations with a small parameter. We assume that this system is the Tikhonov non-homogeneous system with constant coefficients. The paper aims to consider this Cauchy problem, apply the asymptotic method and construct expansions of the solutions in the form of two-type decomposition. This decomposition has regular and border-layer parts. The main result of this paper is a justification of an asymptotic expansion for the solutions of this Cauchy problem. Our method can be applied in a wide variety of cases for singularly perturbed Cauchy problems of Fokker-Planck equations.

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Hydrodynamic limit for the inhomogeneous incompressible Navier-Stokes-Vlasov equations

Yao

et al. 2023

Journal of Differential Equations

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Hydrodynamic limit for the inhomogeneous incompressible Navier-Stokes/Vlasov-Fokker-Planck equations

Cited by 7 publications

References 23 publications

Global derivation of a Boussinesq-Navier-Stokes type system from fluid-kinetic equations

Global derivation of a Boussinesq-Navier-Stokes type system from fluid-kinetic equations

The asymptotic solution of a singularly perturbed Cauchy problem for Fokker-Planck equation

Hydrodynamic limit for the inhomogeneous incompressible Navier-Stokes-Vlasov equations

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