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Dynamic theory for incompressible Smectic-A liquid crystals: Existence and regularity
We study a system that was proposed in [3] in order to
model the dynamic
of Smectic-A liquid crystals. We establish the energy dissipative relation of the system
and prove the existence of global weak solutions. A higher order energy estimate is also
established for the existence of the classical solutions and the regularity of the weak
solutions. Some regularity and stability results are also discussed in this paper.