Abstract

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.

Keywords

  1. bifluid system
  2. Baer--Nunziato system
  3. compressible Navier--Stokes equations
  4. transport equation
  5. continuity equation
  6. renormalized solutions

MSC codes

  1. 76N10
  2. 35Q30

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Information & Authors

Information

Published In

cover image SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis
Pages: 818 - 871
ISSN (online): 1095-7154

History

Submitted: 11 May 2021
Accepted: 25 August 2021
Published online: 7 February 2022

Keywords

  1. bifluid system
  2. Baer--Nunziato system
  3. compressible Navier--Stokes equations
  4. transport equation
  5. continuity equation
  6. renormalized solutions

MSC codes

  1. 76N10
  2. 35Q30

Authors

Affiliations

Funding Information

Distinguished Edurad Cech visiting program
Grantová Agentura České Republiky https://doi.org/10.13039/501100001824 : GA19-04243S
National Research Foundation of Korea https://doi.org/10.13039/501100003725 : NRF2020R1F1A1A01049805

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