Weak-strong uniqueness of incompressible magneto-viscoelastic flows

Zhao, Wenjing

doi:10.3934/cpaa.2020127

Cited by 1 publication

(1 citation statement)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The weak-strong uniqueness of the incompressible viscoelastic model on R 2 with κ = 0 is proved in [23] provided that the initial deformation tensor is close to the identity matrix and the initial velocity is small. On a torus (in dimension two and three), local-in-time existence of strong solutions for a similar non-regularized model is established in [38] extended to a weak-strong uniqueness result in [39] under the assumption that global-in-time existence of weak solutions was known.…”

Section: Bibliographical Remarksmentioning

confidence: 99%

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

et al. 2022

View full text Add to dashboard Cite

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.

show abstract

Section: Bibliographical Remarksmentioning

confidence: 99%