Abels, Helmut and Dolzmann, Georg and Liu, Yuning (2014) WELL-POSEDNESS OF A FULLY COUPLED NAVIER-STOKES/Q-TENSOR SYSTEM WITH INHOMOGENEOUS BOUNDARY DATA. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 46 (4). pp. 3050-3077. ISSN 0036-1410, 1095-7154
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We prove short-time well-posedness and existence of global weak solutions of the Beris-Edwards model for nematic liquid crystals in the case of a bounded domain with inhomogeneous mixed Dirichlet and Neumann boundary conditions. The system consists of the Navier-Stokes equations coupled with an evolution equation for the Q-tensor. The solutions possess higher regularity in time of order one compared to the class of weak solutions with finite energy. This regularity is enough to obtain Lipschitz continuity of the nonlinear terms in the corresponding function spaces. Therefore the well-posedness is shown with the aid of the contraction mapping principle using that the linearized system is an isomorphism between the associated function spaces.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; Beris-Edwards model; liquid crystals; Navier-Stokes equations; Q-tensor; strong-in-time solutions |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 29 Nov 2019 09:06 |
| Last Modified: | 29 Nov 2019 09:06 |
| URI: | https://pred.uni-regensburg.de/id/eprint/10949 |
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