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| In this talk, we focus on a smectic-A liquid crystal model in 3D domains, obtaining three main results: the proof of an adequate Lojasiewicz-Simon inequality in a strong framework, the rigorous proof (via a Galerkin approach) of the existence of global in time weak solutions which are strong (and unique) for large times, and the convergence to equilibrium of the whole trajectory as time goes to infinity. Given any regular initial data, the existence of a unique global in time regular solution (bounded up to infinite time) and the convergence to an equilibrium have been previously proved, but under the constraint of large enough viscosity. Now, all results are obtained without imposing large viscosity. |
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