Vanishing viscosity limit for viscous Burgers-Vlasov equations

TL;DR

This paper proves that solutions of viscous Burgers-Vlasov equations converge to weak solutions of the inviscid equations as viscosity approaches zero, using advanced mathematical techniques.

Contribution

It establishes the vanishing viscosity limit for viscous Burgers-Vlasov equations in a one-dimensional kinetic model, a novel result in this context.

Findings

Convergence of viscous solutions to inviscid weak solutions.

Application of compensated compactness technique.

Use of level set evolution arguments.

Abstract

We establish the vanishing viscosity limit of viscous Burgers-Vlasov equations for one dimensional kinetic model about interactions between a viscous fluid and dispersed particles by using compensated compactness technique and the evolution of level sets arguments. The limit we obtained is exactly a finite-energy weak solution to the inviscid equations.