Article
Convergence to equilibrium for smectic-A liquid crystals in 3D domains without constraints for the viscosity
Author/s | Climent Ezquerra, María Blanca
Guillén González, Francisco Manuel |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2014-06 |
Deposit Date | 2015-10-19 |
Published in |
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Abstract | In this paper, we focus on a smectic-A liquid crystal model in 3D domains, and obtain three main results: the proof of an adequate Lojasiewicz-Simon inequality by using an abstract result; the rigorous proof (via a Galerkin ... In this paper, we focus on a smectic-A liquid crystal model in 3D domains, and obtain three main results: the proof of an adequate Lojasiewicz-Simon inequality by using an abstract result; the rigorous proof (via a Galerkin approach) of the existence of global intime weak solutions that become strong (and unique) in long-time; and its convergence to equilibrium of the whole trajectory as time goes to in nity. Given any regular initial data, the existence of a unique global in-time regular solution (bounded up to in nite time) and the convergence to an equilibrium have been previously proved under the constraint of a su ciently high level of viscosity. Here, all results are obtained without imposing said constraint. |
Citation | Climent Ezquerra, M.B. y Guillén González, F.M. (2014). Convergence to equilibrium for smectic-A liquid crystals in 3D domains without constraints for the viscosity. |
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