Non-homogeneous Navier–Stokes systems with order-parameter-dependent stresses
✍ Scribed by Helmut Abels; Yutaka Terasawa
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 256 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.1264
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✦ Synopsis
Communicated by Y. Shibata
We consider the Navier-Stokes system with variable density and variable viscosity coupled to a transport equation for an order-parameter c. Moreover, an extra stress depending on c and ∇c, which describes surface tension like effects, is included in the Navier-Stokes system. Such a system arises, e.g. for certain models of granular flows and as a diffuse interface model for a two-phase flow of viscous incompressible fluids. The so-called density-dependent Navier-Stokes system is also a special case of our system. We prove short-time existence of strong solution in L q -Sobolev spaces with q>d. We consider the case of a bounded domain and an asymptotically flat layer with a combination of a Dirichlet boundary condition and a free surface boundary condition. The result is based on a maximal regularity result for the linearized system.