Abels, Helmut and Terasawa, Yutaka (2010) Non-homogeneous Navier-Stokes systems with order-parameter-dependent stresses. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 33 (13). pp. 1532-1544. ISSN 0170-4214,
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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 del 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. Copyright (C) 2010 John Wiley & Sons, Ltd.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FLUIDS; DOMAINS; Navier-Stokes equations; free boundary value problems; maximal regularity; diffuse interface models; granular flows; non-stationary Stokes system |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 13 Jul 2020 08:36 |
| Last Modified: | 13 Jul 2020 08:36 |
| URI: | https://pred.uni-regensburg.de/id/eprint/24180 |
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