Viscous compressible homogeneous multi-fluids with multiple velocities: barotropic existence theory

DOI10.17377/semi.2017.14.031zbMath1379.35248arXiv1610.05536MaRDI QIDQ2403683

Alexander E. Mamontov, Dmitriy Alexeyevich Prokudin

Publication date: 11 September 2017

Published in: Sibirskie Èlektronnye Matematicheskie Izvestiya (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.05536

zbMATH Keywords

boundary value problemexistence theoremeffective viscous fluxviscous compressible multi-fluid

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Three or more component flows (76T30) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)

Related Items (7)

Existence of weak solutions to the problem on three-dimensional steady heat-conductive motions of compressible viscous multicomponent mixtures ⋮ Global unique solvability of an initial-boundary value problem for the one-dimensional barotropic equations of binary mixtures of viscous compressible fluids ⋮ Unique solvability of initial-boundary value problem for a model system of equations for the polytropic motion of a mixture of viscous compressible fluids ⋮ Global unique solvability of the initial-boundary value problem for the equations of one-dimensional polytropic flows of viscous compressible multifluids ⋮ Global estimates and solvability of the regularized problem of the three-dimensional unsteady motion of a viscous compressible heat-conductive multifluid ⋮ Unique solvability of initial-boundary value problem for one-dimensional equations of polytropic flows of multicomponent viscous compressible fluids ⋮ Solvability of a regularized boundary-value problem for the system of equations of dynamics of mixtures of viscous compressible heat-conducting fluids

Cites Work

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• Viscous compressible multi-fluids: modeling and multi-D existence
• Solvability of the regularized steady problem of the spatial motions of multicomponent viscous compressible fluids
• Stationary solutions to the equations of dynamics of mixtures of heat-conductive compressible viscous fluids
• Existence of weak solutions to the three-dimensional problem of steady barotropic motions of mixtures of viscous compressible fluids
• Solubility of steady boundary value problem for the equations of polytropic motion of multicomponent viscous compressible fluids
• Solubility of initial boundary value problem for the equations of polytropic motion of multicomponent viscous compressible fluids
• Solvability of a stationary boundary value problem for a model system of the equations of barotropic motion of a mixture of compressible viscous fluids
• Solubility of a stationary boundary-value problem for the equations of motion of a one-temperature mixture of viscous compressible heat-conducting fluids
• Singular limits in thermodynamics of viscous fluids

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