Weak-strong uniqueness for measure-valued solutions to the Ericksen--Leslie model equipped with the Oseen--Frank free energy
- Lasarzik, Robert
2010 Mathematics Subject Classification
- 35Q35 35K52 76A15
- Liquid crystal, Ericksen-Leslie equation, measure-valued solution, weak-strong uniqueness
We analyze the Ericksen-Leslie system equipped with the Oseen--Frank energy in three space dimensions. Recently, the author introduced the concept of measure-valued solutions to this system and showed the global existence of these generalized solutions. In this paper, we show that suitable measure-valued solutions, which fulfill an associated energy inequality, enjoy the weak-strong uniqueness property, i.e. the measure-valued solution agrees with a strong solution if the latter exists. The weak-strong uniqueness is shown by a relative energy inequality for the associated nonconvex energy functional.
- J. Math. Anal. Appl., 470 (2019), pp. 36--90, DOI 10.1016/j.jmaa.2018.09.051 .