Liouville theorem for the steady-state solutions of Q-tensor system of liquid crystal

In this article, we study the steady-state solutions of the coupled Navier-Stokes and Q-tensor system in Rd. We proved the Liouville theorem that u=0,Q=0 with the conditions u∈L3dd−1(Rd)∩Ḣ1(Rd),Q∈H2(Rd) and b2−24ac≤0 (d=2,3).