Nonlinear stability for the three dimensional incompressible flow of nematic liquid crystals

This paper studies the nonlinear stability for the three dimensional incompressible flow of liquid crystals. When the Deborah number γγ is sufficiently small, we show that the linear stability implies the nonlinear stability in (Lp(T3),W1,p(T3)) for all p∈(1,∞)p∈(1,∞).