Global regularity to the 2D non-isothermal inhomogeneous nematic liquid crystal flows

ABSTRACT

In this paper, we prove the global strong solutions for the Cauchy problem of two-dimensional (2D) incompressible non-isothermal nematic liquid crystal flows, if the initial orientation satisfies a geometric condition. Note that the initial data can be arbitrarily large and the initial density can contain vacuum states. When d is a constant vector and $|d|=1$, we also extend the corresponding result in Wang Y. [Global strong solution to the two dimensional nonhomogeneous incompressible heat conducting Navier–Stokes flows with vacuum. Discrete Contin Dyn Syst B. doi:10.3934/dcdsb.2020099.] to the whole space ${\mathbb{R}}^2$, where the global strong solution of 2D inhomogeneous incompressible heat conducting Navier–Stokes flows is established on bounded domain.

Keywords:

• Inhomogeneous case
• non-isothermal nematic liquid crystal flows
• global strong solution
• vacuum

2010 Mathematics Subject Classifications:

• 35Q35
• 76D03
• 76A15

Acknowledgments

We would like to express our sincere appreciation to the editors and anonymous referee for the valuable suggestions and comments in improving the paper. The author is supported by National Natural Science Foundation of China (No. 11901288).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by National Natural Science Foundation of China (Grant Number 11901288).