Global in time solution and time-periodicity for a smectic-A liquid crystal model

Blanca Climent-Ezquerra, Francisco Guillén-González
2010 Communications on Pure and Applied Analysis  
In this paper some results are obtained for a smectic-A liquid crystal model with timedependent boundary Dirichlet data for the so-called layer variable ϕ (the level sets of ϕ 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
more » ... 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.
doi:10.3934/cpaa.2010.9.1473 fatcat:wdlnmyx6zbcuje4kgxi43nqt6a