Time‐periodic solution to the compressible nematic liquid crystal flows in periodic domain

Abstract

In this paper, we consider the time-periodic solution to a simplified version of Ericksen-Leslie equations modeling the compressible hydrodynamic flow of nematic liquid crystals with a time-periodic external force in a periodic domain in R N . By using an approach of parabolic regularization and combining with the topology degree theory, we establish the existence of the time-periodic solution to the model under some smallness and symmetry assumptions on the external force. Then, we give the uniqueness of the periodic solution of this model.

Low Mach number limit of global solutions to 3‐D compressible nematic liquid crystal flows with Dirichlet boundary condition

“…The local existence and uniqueness of classical solution were established by Ma,13 and the global existence of classical solutions to the Cauchy problem was shown in Li et al 14 with smooth initial data that has small energy. For more recent results about the compressible nematic liquid crystal flows, the readers can refer to previous works [15][16][17][18][19][20][21][22] and references therein.…”

Long‐time behavior of solution for the compressible Navier‐Stokes‐Maxwell equations in

“…Recently, Gao et al 5 established the global-in-time existence for the compressible nematic liquid crystal flows in three-dimensional whole space, and time decay rates for the high-order spatial derivatives of density, velocity and director were obtained by using the Green function, energy estimates, and Fourier splitting method. For more results about the Ericksen-Leslie system, the readers can refer to previous studies [6][7][8][9] and references therein. Motivated by the recent work, 5 we hope to establish optimal decay rate for the second-order spatial derivative of solution for the system (2).…”