Abstract:
We consider an initial-boundary value problem describing unsteady barotropic
motions of multi-component mixtures of viscous compressible fluids
in a bounded three-dimensional domain. The material derivative operator is
assumed to be common for all components and determined by the average
velocity of the mixture, but all other terms contain the separate velocities
of the components. The pressure is assumed
to be common and dependent on the total density. We impose no simplifying
assumptions (in particular, on the structure of the viscosity matrix)
besides those stated above and thus preserve all the terms in the equations
that naturally extend the Navier–Stokes model of motions
of one-component media. We prove the existence of weak generalized solutions
of the initial-boundary value problem.
Keywords:
existence theorem, unsteady boundary-value problem, viscous compressible fluid,
homogeneous mixture with multiple velocities, effective viscous flux.
Citation:
A. E. Mamontov, D. A. Prokudin, “Solubility of unsteady equations of multi-component viscous compressible fluids”, Izv. Math., 82:1 (2018), 140–185
This publication is cited in the following 29 articles:
R. V. Brizitskii, “Boundary Value and Control Problems for Mass Transfer Equations with Variable Coefficients”, J Dyn Control Syst, 2024
Evgenii S. Baranovskii, Roman V. Brizitskii, Zhanna Yu. Saritskaia, “Optimal control problems for the reaction–diffusion–convection equation with variable coefficients”, Nonlinear Analysis: Real World Applications, 75 (2024), 103979
D. A. Zakora, “Spectral Properties of Operators in the Problem on Normal Oscillations of a Mixture of Viscous Compressible Fluids”, J Math Sci, 2024
Evgenii S. Baranovskii, Roman V. Brizitskii, Zhanna Yu. Saritskaia, “Boundary Value and Control Problems for the Stationary Heat Transfer Model with Variable Coefficients”, J Dyn Control Syst, 30:3 (2024)
R. V. Brizitskii, “Boundary Value and Control Problems for the Stationary Magnetic Hydrodynamic Equations of Heat Conducting Fluid with Variable Coefficients”, J Dyn Control Syst, 30:4 (2024)
Evgenii S. Baranovskii, Roman V. Brizitskii, Zhanna Yu. Saritskaia, “Multiplicative Control Problem for the Stationary Mass Transfer Model with Variable Coefficients”, Appl Math Optim, 90:2 (2024)
D. A. Zakora, “Spektralnye svoistva operatorov v zadache o normalnykh kolebaniyakh smesi vyazkikh szhimaemykh zhidkostei”, SMFN, 69, no. 1, Rossiiskii universitet druzhby narodov, M., 2023, 73–97
D. A. Zakora, “Zadacha o malykh dvizheniyakh smesi vyazkikh szhimaemykh zhidkostei”, Sib. elektron. matem. izv., 20:2 (2023), 1552–1589
R. V. Brizitskii, Zh. Yu. Saritskaia, “Analysis of inhomogeneous boundary value problems for generalized Boussinesq model of mass transfer”, J. Dyn. Control Syst., 29:4 (2023), 1809–1828
D. A. Zakora, “Spectral properties of the operator in the problem of oscillations in a mixture of viscous compressible fluids”, Diff Equat, 59:4 (2023), 473
G. Alekseev, R. Brizitskii, “Theoretical analysis of boundary value problems for generalized Boussinesq model of mass transfer with variable coefficients”, Symmetry, 14:12 (2022), 2580
M. Bulicek, A. Jüngel, M. Pokorný, N. Zamponi, “Existence analysis of a stationary compressible fluid model for heat-conducting and chemically reacting mixtures”, J. Math. Phys., 63:5 (2022), 051501
Axmann S., Pokorny M., “Steady Solutions to a Model of Compressible Chemically Reacting Fluid With High Density”, Math. Meth. Appl. Sci., 44:8 (2021), 6422–6447
R. V. Brizitskii, Zh. Yu. Saritskaia, “Multiplicative control problems for nonlinear reaction-diffusion-convection model”, J. Dyn. Control Syst., 27:2 (2021), 379–402
A. E. Mamontov, D. A. Prokudin, “Solubility of unsteady equations of the three-dimensional motion of two-component
viscous compressible heat-conducting fluids”, Izv. Math., 85:4 (2021), 755–812
A. E. Mamontov, D. A. Prokudin, “Global unique solvability of an initial-boundary value problem for the one-dimensional barotropic equations of binary mixtures of viscous compressible fluids”, J. Appl. Industr. Math., 15:1 (2021), 50–61
D. A. Prokudin, “Existence of weak solutions to the problem on three-dimensional steady heat-conductive motions of compressible viscous multicomponent mixtures”, Siberian Math. J., 62:5 (2021), 895–907
A E Mamontov, D A Prokudin, “Global unique solvability of the initial-boundary value problem for one-dimensional barotropic equations of viscous compressible bifluids”, J. Phys.: Conf. Ser., 1666:1 (2020), 012032
Zh Saritskaia, P Savinov, “Multiplicative boundary control problems for nonlinear reaction-diffusion-convection model”, J. Phys.: Conf. Ser., 1666:1 (2020), 012045
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