Andrei Tarfulea : Improved estimates for thermal fluid equations

Posted by Mimi Dai , part of the Analysis and Applied Mathematics Seminar.

At

Feb. 20, 2017, 4 p.m.

In

SEO 636

Abstract

We consider a model for three-dimensional fluid flow on the torus that also keeps track of the local temperature. The momentum equation is the same as for Navier-Stokes, however the kinematic viscosity grows as a function of the local temperature. The temperature is, in turn, fed by the local dissipation of kinetic energy. Intuitively, this leads to a mechanism whereby turbulent regions increase their local viscosity and dissipate faster. We prove a strong a priori bound (that would fall within the Ladyzhenskaya-Prodi-Serrin criterion for ordinary Navier-Stokes) on the thermally weighted enstrophy for classical solutions to the coupled system.