Ill-Posedness / Well-Posedness Results for a Class of Active Scalar Equations
Speaker: Susan Friedlander
Location: Warren Weaver Hall 1302
Date: Thursday, November 7, 2013, 11 a.m.
We discuss a class of active scalar equations where the transport velocities are more singular than the active scalar. There is a significant difference in the well-posedness properties of the problem depending on whether the Fourier multiplier symbol for the velocity is even or odd. The "even" symbol non-diffusive or weakly diffusive equations are ill-posed in Sobolev spaces. However the critically diffusive equations are globally well posed in both the odd and even cases.
Examples of "even" equations are the magnetogeostrophic equation that is a model for the geodynamo and the modified porous media equation.
This is joint work with Francisco Gancedo, Weiran Sun and Vlad Vicol.