### Wellposedness of a Coupled Navier-Stokes/Q-tensor System

Liu, Y *(Universität Regensburg)*

Tuesday 09 April 2013, 15:30-16:00

Satellite

#### Abstract

In this work, we show the existence and uniqueness of local strong solution for a coupled Navier-Stokes/Q-tensor system on a bounded domain $\Omega\subset\mathbb{R}^3$ with Dirichlet boundary condition. One of the novelties brought in with respect to the existing literature consists in the fact that we deal with Navier-Stokes equation with variable viscosity. Concerning the methodology, we use an approximation method to handle the linearized system and the existence of solution to the nonlinear system is proved via a Banach's fixed point argument, based on the estimates on the lower order terms.

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