3 papers
math.AP2024
Exponential scalar mixing for the 2D Navier-Stokes equations with degenerate stochastic forcing
William Cooperman, Keefer Rowan
We show exponential mixing of passive scalars advected by a solution to the stochastic Navier-Stokes equations with finitely many (e.g. four) forced modes satisfying a hypoelliptic…
math.AP2023
Slow periodic homogenization for Hamilton-Jacobi equations
William Cooperman
Capuzzo-Dolcetta and Ishii proved that the rate of periodic homogenization for coercive Hamilton-Jacobi equations is . We complement this result by constructi…
math.AP2022
Exponential mixing by shear flows
William Cooperman
We prove a version of Bressan's mixing conjecture where the advecting field is constrained to be a shear at each time. Also, inspired by recent work of Blumenthal, Coti Zelati and…