Analysis and Applied Mathematics Seminar
Andrei Tarfulea
University of Chicago
Improved estimates for thermal fluid equations
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.
Monday February 20, 2017 at 4:00 PM in SEO 636