Lyapunov exponents and asymptotic mixing in the DiPerna-Lions flow

In 2003, A. Bressan proposed a conjecture concerning the mixing efficiency of incompressible flows, which remains open. I will survey progress toward its resolution and present a new result establishing the asymptotic validity of the conjecture for time-periodic velocity fields. This is achieved by adapting tools from smooth ergodic theory, such as Lyapunov exponents, to the non-smooth setting of DiPerna-Lions flows.