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Mathematics > Analysis of PDEs

arXiv:2108.03094 (math)
[Submitted on 6 Aug 2021]

Title:Strong well-posedness, stability and optimal control theory for a mathematical model for magneto-viscoelastic fluids

Authors:Harald Garcke, Patrik Knopf, Sourav Mitra, Anja Schlömerkemper
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Abstract: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.
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Optimization and Control (math.OC)
MSC classes: 35Q35, 35Q60, 49J20, 49K20, 76A10, 76D05
Cite as: arXiv:2108.03094 [math.AP]
  (or arXiv:2108.03094v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.2108.03094

Submission history

From: Sourav Mitra [view email]
[v1] Fri, 6 Aug 2021 13:01:21 UTC (47 KB)
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