Title
Transport by Sobolev vector fields: regularity and asymptotic mixing
Abstract
In 1989, DiPerna and Lions developed a well-posedness theory for bounded solutions of transport equations driven by Sobolev vector fields.
A related conjecture on mixing efficiency in incompressible flows was formulated by Bressan in 2003 and remains open.
First, I will review the existing well-posedness theory and discuss recent developments in regularity theory, including a new result.
Then, I will survey progress on Bressan’s mixing conjecture and present a new result establishing its asymptotic validity for time-periodic vector fields.
This result is obtained by adapting tools from smooth ergodic theory, such as Lyapunov exponents, to the non-smooth setting of regular Lagrangian flows.
The talk is based on joint work with Elia Brué, Maria Colombo and Guido De Philippis.
A related conjecture on mixing efficiency in incompressible flows was formulated by Bressan in 2003 and remains open.
First, I will review the existing well-posedness theory and discuss recent developments in regularity theory, including a new result.
Then, I will survey progress on Bressan’s mixing conjecture and present a new result establishing its asymptotic validity for time-periodic vector fields.
This result is obtained by adapting tools from smooth ergodic theory, such as Lyapunov exponents, to the non-smooth setting of regular Lagrangian flows.
The talk is based on joint work with Elia Brué, Maria Colombo and Guido De Philippis.
Please note that the seminar will take place in person in room 140 of Huxley Building.