Article
Global in time solution and time-periodicity for a smectic-A liquid crystal model
Author/s | Climent Ezquerra, María Blanca
Guillén González, Francisco Manuel |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2010 |
Deposit Date | 2016-03-30 |
Published in |
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Abstract | 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 φ (the level sets of φ describe the layer structure of the smectic-A ... 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 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 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. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España Junta de Andalucía |
Project ID. | MTM2006–07932
P06-FQM-02373 |
Citation | Climent Ezquerra, M.B. y Guillén González, F.M. (2010). Global in time solution and time-periodicity for a smectic-A liquid crystal model. Communications on Pure and Applied Analysis, 9 (6), 1473-1493. |
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