Existence and uniqueness of solutions to a model describing miscible liquids. (Existence et unicité des solutions pour un modèle décrivant les liquides miscibles.) (English. French summary) Zbl 1375.76032
Summary: The existence and the uniqueness of solutions to a problem of miscible liquids are investigated in this note. The model consists of Navier-Stokes equations with Korteweg stress terms coupled with the reaction-diffusion equation for the concentration. We assume that the fluid is incompressible and the Boussinesq approximation is adopted. The global existence and uniqueness of solutions is established for some optimal conditions on the reaction source term and the external force functions.
MSC:
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
References:
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