## View abstract

### Session S37 - New Developments in Mathematical Fluid Dynamics

Monday, July 19, 19:00 ~ 19:25 UTC-3

## The limit Euler-$\alpha$ to Euler in domains with boundary

### MILTON Lopes Filho

#### Universidade Federal do Rio de Janeiro, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak1cc2aed09a8697afc0256b33f0951875').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy1cc2aed09a8697afc0256b33f0951875 = 'ml&#111;p&#101;s' + '&#64;'; addy1cc2aed09a8697afc0256b33f0951875 = addy1cc2aed09a8697afc0256b33f0951875 + '&#105;m' + '&#46;' + '&#117;frj' + '&#46;' + 'br'; var addy_text1cc2aed09a8697afc0256b33f0951875 = 'ml&#111;p&#101;s' + '&#64;' + '&#105;m' + '&#46;' + '&#117;frj' + '&#46;' + 'br';document.getElementById('cloak1cc2aed09a8697afc0256b33f0951875').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy1cc2aed09a8697afc0256b33f0951875 + '\'>'+addy_text1cc2aed09a8697afc0256b33f0951875+'<\/a>';

The Euler-$\alpha$ equations are a regularization of the incompressible Euler system, obtained by dynamical averaging of small scales. The problem of identifying the limiting behavior of solutions when $\alpha \to 0$ is similar to the analogous problem for vanishing viscosity, but with important differences. In this talk we discuss several results concerning this limit, assuming no-slip boundary conditions and initial data increasingly irregular.

Joint work with Adriana Valentina Busuioc (U. St. Etienne), Dragos Iftimie (U. Lyon) and Helena Nussenzveig Lopes (UFRJ).