Weak-strong uniqueness for measure-valued solutions to the Ericksen-Leslie model equipped with the Oseen-Frank free energy
arXiv:1711.03371 · doi:10.1016/j.jmaa.2018.09.051
Abstract
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.
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Cited by in corpus (10)
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- Measure-valued solutions to the Ericksen-Leslie model equipped with the Oseen-Frank energy
- Dissipative solution to the Ericksen-Leslie system equipped with the Oseen-Frank energy
- Well-posedness of the Ericksen-Leslie System for the Oseen-Frank Model in L^3_{uloc}(\mathbb{R}^3)
- Approximation and optimal control of dissipative solutions to the Ericksen--Leslie system
- Analysis of a thermodynamically consistent Navier--Stokes--Cahn--Hilliard model
- Weak-strong uniqueness for the general Ericksen-Leslie system in three dimensions
- On the existence of weak solutions in the context of multidimensional incompressible fluid dynamics
- Analysis and numerical approximation of energy-variational solutions to the Ericksen--Leslie equations
- Existence of weak solutions to a dynamic model for smectic-A liquid crystals under undulations