Stochastic and Multiscale Modeling and Computation Seminar by Yuanzhen Shao: Thermodynamically Consistent Models for Non-Isothermal Magnetoviscoelastic Fluids

Title: Thermodynamically Consistent Models for Non-Isothermal Magnetoviscoelastic Fluids

 

Abstract: In this talk, we consider the motion of a magnetoviscoelastic fluid in a non-isothermal environment. When the deformation tensor field is governed by a regularized transport equation, the motion of the fluid can be described by a quasilinear parabolic system. We will establish the local existence and uniqueness of a strong solution. Then it will be shown that a solution initially close to a constant equilibrium exists globally and converges to a (possibly different) constant equilibrium. Further, we will show that every solution that is eventually bounded in the topology of the natural state space exists globally and converges to the set of equilibria. If time permits, we will discuss some recent advancements regarding the scenario where the deformation tensor is modeled by a transport equation. In particular, we will discuss the local existence and uniqueness of a strong solution as well as global existence for small initial data.