Speaker
Description
This talk is concerned with describing the dynamics of a dilute plasma which has a very low electrical resistance $\mu = \epsilon$ and a comparatively large viscosity, e.g. the Solar corona, Solar wind, or some laboratory plasmas. In this situation, has been conjectured by physicists Woltjer (1958) and Taylor (1974-1986) that the fluid undergoes a two stage dynamic.
In a first stage, on a time scale $t \sim \log \frac{1}{\epsilon}$, the large viscosity drives the plasma to a force-free state, where the Laplace force acting on the fluid is small $j \times b = O(\epsilon)$. In a second stage of evolution, on a time scale $t \sim \frac{1}{\epsilon}$, the resistivity drives the evolution.
This conjecture has proven very very difficult to verify, by theoretical, numerical or even experimental arguments. By working on a 1D magneto-Stokes model, we will show rigorously that a two stage process does indeed take place in that setting. Moreover, we derive effective equations for the dynamics of the resistivity driven stage, and prove that the solutions of these equations may blowup in finite time.
This is joint work with Daniel Sánchez-Simón del Pino and Juan J. L. Velázquez (Universität Bonn).
