Applied Mathematics Seminar
Helena J. Nussenzveig Lopes
Universidade Federal do Rio de Janeiro
On the convergence of 2D second-grade fluid and Euler-alpha equations to Euler equations in bounded domains
Abstract: Second-grade fluid equations are a simple model for viscoelastic fluids with two parameters: viscosity $\nu >0$ and
elastic response
$\alpha > 0$. Setting $\nu = 0$ reduces to the Euler-alpha equations, which are a regularization of the incompressible
Euler equations, while setting $\alpha = 0$ reduces to the Navier-Stokes equations. Formally setting both
$\alpha$ and $\nu$ to vanish
reduces to the Euler equations.
We consider both the second-grade fluid equations and the Euler-alpha equations in a smooth, bounded domain, under no-slip boundary conditions. For a suitably defined converging family of initial data we consider a corresponding family of solutions t
o these equations
, depending on
$\alpha$ and $\nu$. We examine the limits of vanishing $\alpha$ and $\nu$ and we obtain, for certain regimes, convergence to solutions of the incompressible Euler equations, while in other regimes we obtain sharp criteria for convergence, analogous to Kato's criterion. This talk is based on joint work with M. C. Lopes Filho, E. S. Titi and A. Zang.
Monday April 20, 2015 at 3:00 PM in SEO 636