On temporal decay estimates for the compressible nematic liquid crystal flow in

Abstract

We use a general energy method recently developed by [Guo Y, Wang Y. Decay of dissipative equations and negative sobolev spaces. Commun. Partial Differ. Equ. 2012;37:2165–2208.] to prove the global existence and temporal decay rates of solutions to the three-dimensional compressible nematic liquid crystal flow in the whole space. In particular, the negative Sobolev norms of solutions are shown to be preserved along time evolution, and then the optimal decay rates of the higher order spatial derivatives of solutions are obtained by energy estimates and the interpolation inequalities.

Keywords:

• Compressible nematic liquid crystal flow
• temporal decay estimates
• energy estimates
• negative Sobolev space

AMS Subject Classifications:

• 76A15
• 35B65
• 35Q35

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China [grant number 11326155], [grant number 11401202]; the Scientific Research Fund of Hunan Provincial Education Department [grant number 14B117]; the China Postdoctoral Science Foundation [grant number 2015M570053].