Speaker
Konstantin Kalinin
Description
We start by demonstrating that the interplay between advection and diffusion in the incompressible porous media equation with diffusion -- a classical active scalar transport equation -- can lead to the enhanced dissipation. Subsequently, we derive a scaling limit that perfectly balances these two physical mechanisms. The high degeneracy of the limiting equation prevents us from proving existence of weak solutions in the distributional sense. To address this challenge and finish the existence proof, we use the gradient flow structure of the equation to define weak solutions within a more robust "geometric" framework.
