Young Researchers Workshop: Current trends in kinetic theory

Compactness and weak solutions of time fractional PDEs

Lei Li

Duke University
[SLIDES]

The Aubin-Lions lemma and its variants play crucial roles for the existence of weak solutions of nonlinear evolutionary PDEs. I will talk about some compactness criteria that are analogies of Aubin-Lions lemma for the existence of weak solutions to time fractional PDEs. The existence of weak solutions for a special case of time fractional compressible Navier-Stokes equations with constant density and time fractional Keller-Segel equations in $R^2$ are then studied as model problems.