Communications in Mathematical Sciences
Volume 18 (2020)
Vanishing viscosity limit for viscous Burgers–Vlasov equations
Pages: 1135 – 1148
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