The $\mathcal{R}$-boundedness of solution operators for the $Q$-tensor model of nematic liquid crystals

In this paper, we consider a resolvent problem arising from the $Q$-tensor model for liquid crystal flows in the half-space. Our purpose is to show the $\mathcal{R}$-boundedness for the solution operator families of the resolvent problem when the resolvent parameter lies near the origin. The definit