Hardy space theory of compensated compactness quantities and an application to 2D magnetohydrodynamics

The topic of the talk is the Hardy space theory of compensated compactness quantities which originated in the seminal paper of Coifman, Lions, Meyer and Semmes from 1993. I concentrate on quantities relevant to fluid dynamics and discuss the relation between compensated compactness and Hardy space integrability. I also present an application to uniqueness of weak solutions with vanishing Cauchy data in 2D magnetohydrodynamics, which is joint work with Daniel Faraco.