Young Measures and Order‐Disorder Transition in Stationary Flow of Liquid Crystals

Autor:	Maria-Carme Calderer, Alexander Panchenko
Rok vydání:	2007
Předmět:	Applied Mathematics Weak solution Degenerate energy levels Mathematical analysis Hagen–Poiseuille equation Physics::Fluid Dynamics Computational Mathematics Nonlinear system Classical mechanics Liquid crystal Ordinary differential equation Newtonian fluid Analysis Young measure Mathematics
Zdroj:	SIAM Journal on Mathematical Analysis. 38:1642-1659
ISSN:	1095-7154 0036-1410
Popis:	We study a system of nonlinear second order ordinary differential equations modeling Poiseuille flow of liquid crystals with variable degree of orientation, at the limit of large Ericksen number. The system is singularly perturbed and degenerate, and as a result the solutions are highly oscillatory. We obtain the relations satisfied by the Young measures generated by sequences of weak solutions, and show that the persistent oscillations are encoded in the Young measure generated by the molecular alignment variable. The effective equations correspond to the macroscopic isotropic Newtonian flow with a liquid crystalline microstructure indicating a remnant alignment.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::7d3186e4fcffcaf154074dd3273f9132 https://doi.org/10.1137/050623735 Zobrazit plný text záznamu