Garcke, Harald and Knopf, Patrik and Mitra, Sourav and Schlömerkemper, Anja (2022) Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 61 (5): 179. ISSN 0944-2669, 1432-0835
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In this article, we study the strong well-posedness, stability and optimal control of an incompressible magneto-viscoelastic fluid model in two dimensions. The model consists of an incompressible Navier-Stokes equation for the velocity field, an evolution equation for the deformation tensor, and a gradient flow equation for the magnetization vector. First, we prove that the model under consideration posseses a global strong solution in a suitable functional framework. Second, we derive stability estimates with respect to an external magnetic field. Based on the stability estimates we use the external magnetic field as the control to minimize a cost functional of tracking-type. We prove existence of an optimal control and derive first-order necessary optimality conditions. Finally, we consider a second optimal control problem, where the external magnetic field, which represents the control, is generated by a finite number of fixed magnetic field coils.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | OPTIMAL BOUNDARY CONTROL; WEAK-STRONG UNIQUENESS; LIQUID-CRYSTAL FLOWS; NAVIER-STOKES SYSTEM; LONG-TIME BEHAVIOR; EVOLUTIONARY MODEL; EXISTENCE |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 07 Feb 2024 07:47 |
| Last Modified: | 07 Feb 2024 07:47 |
| URI: | https://pred.uni-regensburg.de/id/eprint/56901 |
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