Communications in Mathematical Sciences

Volume 18 (2020)

Number 4

Vanishing viscosity limit for viscous Burgers–Vlasov equations

Pages: 1135 – 1148



Wentao Cao (Institute für Mathematik, Universität Leipzig, Germany)

Teng Wang (Faculty of Science, School of Mathematics, Beijing University of Technology, Beijing, China)


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.


vanishing viscosity limit, two phase flow, Vlasov equation, Burgers equation, finite-energy weak solution

2010 Mathematics Subject Classification

35F20, 35Q35, 45K05, 76T10, 82D05

The research of W. Cao is supported by ERC Grant Agreement No. 724298. The work of T. Wang is partially supported by NNSFC grant No. 11971044 and BJNSF grant No. 1202002.

Received 18 April 2019

Accepted 22 January 2020

Published 28 July 2020