Differential Equations Seminar

We will discuss a recent construction of self-similar blow-up for C^{1,a} solutions to the incompressible Euler equation for small a>0. This is done by isolating a simple non-linear equation that encodes the leading order dynamics of solutions to the Euler equation in certain regimes. The model also has explicit stable self-similar solutions. The self-similar solutions to the Euler equation also turn out to be stable with respect to certain perturbations. This allows us to deduce finite-time singularity formation for localized (finite-energy) C^{1,a} solutions. A part of what we will discuss is joint work with T. Ghoul and N. Masmoudi. Speaker(s): Tarek Elgindi (UC San Diego)