GLOBAL IN TIME SOLUTION AND TIME-PERIODICITY FOR A SMECTIC-A LIQUID CRYSTAL MODEL

In this paper some results are obtained for a smectic-A liquid crystal model with time-dependent boundary Dirichlet data for the so-called layer variable phi (the level sets of phi describe the layer structure of the smectic-A liquid crystal). First, the initial-boundary problem for arbitrary initial data is considered, obtaining the existence of weak solutions which are bounded up to infinity time. Second, the existence of time-periodic weak solutions is proved. Afterwards, the problem of the global in time regularity is attacked, obtaining the existence and uniqueness of regular solutions ( up to infinity time) for both problems, i.e. the initial-valued problem and the time-periodic one, but assuming a dominant viscosity coefficient in the linear part of the diffusion tensor.