Incompressible Limit of the Compressible Q-tensor System of Liquid Crystals  

作　　者：Yi-xuan WANG 

机构地区：[1]University of Pittsburgh,PA 15260,USA

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第1期179-201,共23页应用数学学报（英文版）

基　　金：supported in part by the NSF grant DMS-1907519。

摘　　要：We study the connection between the compressible Navier-Stokes equations coupled by the Qtensor equation for liquid crystals with the incompressible system in the periodic case, when the Mach number is low. To be more specific, the convergence of the weak solutions of the compressible nematic liquid crystal model to the incompressible one is proved as the Mach number approaches zero, and we also obtain the similar results in the stochastic setting when the equations are driven by a stochastic force. Our approach is based on the uniform estimates of the weak solutions and the martingale solutions, then we justify the limits using various compactness criteria.

关 键 词：compressible liquid crystal system Q-tensor weak solutions martingale solution stochastic compactness Mach number incompressible limit 

分 类 号：O175[理学—数学]