Weak solutions for a bifluid model for a mixture of two compressible noninteracting fluids with general boundary data

0554415 - MÚ 2023 RIV US eng J - Journal Article
Kračmar, Stanislav - Kwon, Y.-S. - Nečasová, Šárka - Novotný, A.
Weak solutions for a bifluid model for a mixture of two compressible noninteracting fluids with general boundary data.
SIAM Journal on Mathematical Analysis. Roč. 54, č. 1 (2022), s. 818-871. ISSN 0036-1410. E-ISSN 1095-7154
R&D Projects: GA ČR(CZ) GA19-04243S
Institutional support: RVO:67985840
Keywords : bifluid system * Baer-Nunziato system * compressible Navier-Stokes equations * transport equation
OECD category: Pure mathematics
Impact factor: 2, year: 2022
Method of publishing: Limited access
https://doi.org/10.1137/21M1419246

We prove global existence of weak solutions for a version of the one velocity Baer--Nunziato system with dissipation describing a mixture of two noninteracting viscous compressible fluids in a piecewise regular Lipschitz domain with general inflow/outflow boundary conditions. The geometrical setting is general enough to comply with most current domains important for applications, such as (curved) pipes of piecewise regular and axis-dependent cross-sections. For the existence proof, we adapt to the system the 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, and Yu [J. Math. Pures Appl. (9), 125 (2019), pp. 247--282]. The results related to the families of transport equations presented in this paper extend/improve some statements of the theory of renormalized solutions and are therefore of independent interest.
Permanent Link: http://hdl.handle.net/11104/0329121