ASYMPTOTIC BEHAVIOR OF NON-ISOTHERMAL COMPRESSIBLE NEMATIC LIQUID-CRYSTAL FLOWS IN AN INFINITE LAYER

抄録

The non-isothermal model of compressible nematic liquid crystals in a three-dimensional infinite layer is considered. We prove the existence of global strong solutions and their decay rates when the initial data is close to steady state. It turns out that the low-frequency part of the solution decays like a two-dimensional heat kernel. We can also see that the low-frequency part appears in the asymptotic reading part of the solution which is affected by nonlinear terms as t goes to infinity.