Weak solutions for a bi-fluid model for a mixture of two compressible\n non interacting fluids with general boundary data

2021/05/11 by Stanislav Kracmar, Kracmar, Stanislav, Young-Sam Kwon +5
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2105.04843

openalex publication_date 2021/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove global existence of weak solutions for a version of one velocity\nBaer-Nunziato system with dissipation describing a mixture of two non\ninteracting viscous compressible fluids in a piecewise regular Lipschitz domain\nwith general inflow/outfow boundary conditions. The geometrical setting is\ngeneral enough to comply with most current domains important for applications\nas, for example, (curved) pipes of picewise regular and axis-dependent cross\nsections. As far as the existence proof is concerned, we adapt to the system\nthe nowaday's classical Lions-Feireisl approach to the compressible\nNavier-Stokes equations which is combined with a generalization of the theory\nof renormalized solutions to the transport equations in the spirit of\nVasseur-Wen-Yu. The results related to the families of transport equations\npresented in this paper extend/improve some of statements of the theory of\nrenormalized solutions, and they are therefore of independent interest.\n

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