- Rene Cabrera
- University of Texas, Austin
- Date: Nov. 20, Wednesday, 2024
- Time: 11:00am -- 11:50am
- Host: Yuming Paul Zhang
- Room: Parker 328
- Abstract: The Landau-Coulomb equation is regarded as one of the most studied equations in PDEs. It models the evolution of a particle distribution in the theory of collisional plasma. We focus on the diffusion operator within the equation only. With this diffusion term, this equation contains a reaction term that could rapidly transform "nice" configurations into singularities. In this talk, we’ll give a brief history regarding well posedness of this equation, then present a result regarding the diffusion operator in the Landau-Coulomb equation that provides much stronger regularization effects than its linear counterpart, the Laplace operator. This is work in collaboration with Maria Gualdani and Nestor Guillen.