Communications in Mathematical Sciences

Volume 13 (2015)

Number 8

Multicomponent mixture model: the issue of existence via time discretization

Pages: 1975 – 2003



Ewelina Zatorska (Institute of Mathematics of Polish Academy of Sciences, Warsaw, Poland)

Piotr Bogusław Mucha (Institute of Applied Mathematics and Mechanics, University of Warsaw, Poland)


We prove the existence of global-in-time weak solutions to a model of chemically reacting mixture. We consider a coupling between the compressible Navier–Stokes system and the reaction diffusion equations for chemical species when the thermal effects are neglected. We first prove the existence of weak solutions to the semi-discretization in time. Based on this, the existence of solutions to the evolutionary system is proven.


weak solutions to compressible flows, mixture models, time discretization, chemically reacting gases, barotropic flows

2010 Mathematics Subject Classification

35B45, 35D30, 76N10

Published 3 September 2015