Weak solutions for a bi-fluid model for a mixture of two compressible non interacting fluids with general boundary data
Abstract
We prove global existence of weak solutions for a version of one velocity Baer-Nunziato system with dissipation describing a mixture of two non interacting viscous compressible fluids in a piecewise regular Lipschitz domain with general inflow/outfow boundary conditions. The geometrical setting is general enough to comply with most current domains important for applications as, for example, (curved) pipes of picewise regular and axis-dependent cross sections. As far as the existence proof is concerned, we adapt to the system the nowaday's classical Lions-Feireisl approach to the compressible Navier-Stokes equations which is combined with a generalization of the theory of renormalized solutions to the transport equations in the spirit of Vasseur-Wen-Yu. The results related to the families of transport equations presented in this paper extend/improve some of statements of the theory of renormalized solutions, and they are therefore of independent interest.
Keywords
Cite
@article{arxiv.2105.04843,
title = {Weak solutions for a bi-fluid model for a mixture of two compressible non interacting fluids with general boundary data},
author = {Stanislav Kracmar and Young-Sam Kwon and Sarka Necasova and Antonin Novotny},
journal= {arXiv preprint arXiv:2105.04843},
year = {2021}
}