MLC

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.