On stationary motions of Prandtl-Eyring fluids in 2D

On stationary motions of Prandtl-Eyring fluids in 2D

Thu, 19/05/2011
12:30 		Dominic Breit (University of Saarbrucken) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
On stationary motions of Prandtl-Eyring fluids in 2D
We prove the existence of weak solutions to steady Navier Stokes equations
$$\text{div}\, \sigma+f=\nabla\pi+(\nabla u)u.$$
Here $ u:\mathbb{R}^2\supset \Omega\rightarrow \mathbb{R}^2 $ denotes the velocity field satisfying $ \text{div}\, u=0 $, $ f:\Omega\rightarrow\mathbb{R}^2 $ and $ \pi:\Omega\rightarrow\mathbb{R} $ are external volume force and pressure, respectively. In order to model the behavior of Prandtl-Eyring fluids we assume
$$\sigma= DW(\varepsilon (u)),\quad W(\varepsilon)=|\varepsilon|\log (1+|\varepsilon|).$$
A crucial tool in our approach is a modified Lipschitz truncation preserving the divergence of a given function.