# Global existence and regularity for the full coupled Navier-Stokes and Q-tensor system - Mathematics > Analysis of PDEs

Global existence and regularity for the full coupled Navier-Stokes and Q-tensor system - Mathematics > Analysis of PDEs - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: We study the global existence and regularity of solutions for a systemdescribing the evolution of a nematic liquid crystal fluid. The fluid isdescribed by a system that couples a forced Navier-Stokes system with aparabolic-type system. In our previous work, \cite{pz1}, we assumed that acertain parameter, $\xi$, is zero, which had the effect of cancelling certainterms. In the current work we do not make this assumption and study the fullsystem, observing that the presence of these additional terms has a non-trivialeffect, namely the quadruply exponential increase of the high norms. We alsoestimate differently certain terms already existent in the simplified systemand improve the estimates in \cite{pz1}. We prove the existence of global weaksolutions in dimensions two and three. In dimension two we prove the higherregularity of solutions and show that the high norms increase in time at mostquadruply exponential. We also show the weak-strong uniqueness in dimensiontwo.

Autor: Marius Paicu, Arghir Zarnescu

Fuente: https://arxiv.org/