Decay for the equations of compressible flow of nematic liquid crystals.

It is well-known that the Cauchy problem of the compressible liquid crystals flow admits a unique global-in-time solution, belonging to C 0 (R 0 + , H l (R 3)) with l ⩾ 3 ; moreover the lower-order or higher-order derivative of solution enjoys the same decay-in-time rate as well as the linear solution (i.e., the solution of the corresponding linear problem). In this paper we further prove that highest-order derivative of the unique solution also enjoys the same decay-in-time rate as well as the linear solution by developing new analytical skills. In other words, the optimal decay rate for the highest-order derivative of solution can be also obtained. [ABSTRACT FROM AUTHOR]