Incompressible limit for compressible nematic liquid crystal flows in a bounded domain

ABSTRACT

In this paper, we consider the incompressible limit of strong solution for the compressible nematic liquid crystal flows in a 3D bounded domain $\mathrm{\Omega }\subset {\mathbb{R}}^3$ where the the velocity field satisfies the Dirichlet boundary condition. We establish the uniform estimates with respect to the Mach number for the strong solutions with large initial data in a short time interval. Consequently, we obtain the convergence of the compressible nematic liquid crystal system to the incompressible nematic liquid crystals system as the Mach number tends to zero.

COMMUNICATED BY:

• Adrian Constantin

KEYWORDS:

• Incompressible limit
• compressible nematic liquid crystal equations
• Dirichlet boundary condition

MSC:

• 35Q35
• 35M33
• 75A15

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by NSFC [grant numbers 11731014, 11571254] and by Science Challenge Project [grant number TZ2016002].