Analysis and numerical approximation of energy-variational solutions to the Ericksen–Leslie equations

10/31/2022
by   Robert Lasarzik, et al.
0

We define the concept of energy-variational solutions for the Ericksen–Leslie equations in three spatial dimensions. This solution concept is finer than dissipative solutions and satisfies the weak-strong uniqueness property. For a certain choice of the regularity weight, the existence of energy-variational solutions implies the existence of measure-valued solutions and for a different choice, we construct an energy-variational solution with the help of an implementable, structure-inheriting space-time discretization. Computational studies are performed in order to provide some evidence of the applicability of the proposed algorithm.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset