On a Model for Mixture Flows: Derivation, Dissipation and Stability Properties

We propose a new model describing mixture flows. The non linear system couples heterogeneous Navier–Stokes equations with a constraint on the mean volume velocity of the flow. The PDE system is obtained from a more microscopic viewpoint, involving a Vlasov-like equation describing the disperse phase...

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Bibliographic Details
Published in:Archive for rational mechanics and analysis 2016-04, Vol.220 (1), p.1-35
Main Authors: Goudon, Thierry, Vasseur, Alexis
Format: Article
Language:English
Subjects:
Analysis of PDEs
Classical Mechanics
Complex Systems
Computational fluid dynamics
Derivation
Dissipation
Fluid- and Aerodynamics
Linear systems
Mathematical analysis
Mathematical and Computational Physics
Mathematical models
Mathematics
Navier-Stokes equations
Physics
Physics and Astronomy
Properties (attributes)
Stability
Theoretical
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Summary:We propose a new model describing mixture flows. The non linear system couples heterogeneous Navier–Stokes equations with a constraint on the mean volume velocity of the flow. The PDE system is obtained from a more microscopic viewpoint, involving a Vlasov-like equation describing the disperse phase, through a certain hydrodynamic limit. The model has remarkable dissipation properties, inherited from the structure of the fluid-kinetic description. Based on these properties, together with additional estimates that can be obtained in the one-dimension framework, we establish the stability of weak solutions.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-015-0925-3