Incompressible limit of the Ericksen-Leslie hyperbolic liquid crystal model in compressible flow

Liang Guo, Ning Jiang, Fucai Li, Yi-Long Luo, Shaojun Tang

Published 2019-11-11Version 1

We justify the incompressible limit of the Ericksen-Leslie hyperbolic liquid crystal model in compressible flow in the framework of classical solutions. We first derive the uniform energy estimates on the Mach number $\eps$ for both the compressible system and its differential system with respect to time under uniformly in $\eps$ small initial data. Then, based on these uniform estimates, we pass to the limit $\eps \rightarrow 0$ in the compressible system, so that we establish the global classical solution of the incompressible system by the compactness arguments. Moreover, we also obtain the convergence rates associated with $L^2$-norm in the case of well-prepared initial data.