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.

 

 

Faculty host: Yuming Paul Zhang