| Abstract: |
| In this talk we study the well-posedness for the mildly compressible Navier-Stokes-Cahn-Hilliard system with non-constant viscosity and Landau potential in two and three dimensional domains.
Navier-Stokes-Cahn-Hilliard (NSCH) type systems arise from the Diffuse Interface (DI) theory. In fluid mechanics the Diffuse Interface theory (DI) has been widely used in the last decades to describe the motion of binary fluid mixtures and their topological transitions under the effect of the surface tension. The main advantages of the DI formulation are twofold: DI models can be regarded as a regularization of the free boundary models with the purpose of approximating the limit problem as the interface thickness converges to zero, and DI methods provide a realistic description of complex fluids (e.g. polymers and gels).
The original NSCH system deals with homogeneous (constant density) and incompressible binary mixtures. This system has been extensively studied in the last years.
The development of NSCH systems for non-homogeneous binary mixtures has started with the seminal paper by Lowengrub and Truskinovsky (1998). As a step toward the study of the more complex models proposed by Lowengrub and Truskinovsky, we consider here the case where the fluid is mildly compressible. Various results of existence and uniqueness of solutions in 2 and 3 space dimensions are derived. |
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