Abstract
AbstractIn this paper, we prove the global well posedness and the decay estimates for a $${\mathbb {Q}}$$
Q
-tensor model of nematic liquid crystals in $$\mathbb {R}^N$$
R
N
, $$N \ge 3$$
N
≥
3
. This system is a coupled system by the Navier–Stokes equations with a parabolic-type equation describing the evolution of the director fields $${\mathbb {Q}}$$
Q
. The proof is based on the maximal $$L_p$$
L
p
–$$L_q$$
L
q
regularity and the $$L_p$$
L
p
–$$L_q$$
L
q
decay estimates to the linearized problem.
Funder
Japan Society for the Promotion of Science
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics,Condensed Matter Physics,Mathematical Physics
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