We will discuss some old and new results concerning the
long-time behavior of solutions to the two-dimensional
incompressible Euler equations. Specifically, we discuss
whether steady states can be isolated, wandering for solutions
starting nearby...
In this three-part lecture series, we will present a series of
works by Bedrossian, Blumenthal and Punshon-Smith on the chaotic
mixing and enhanced dissipation properties of a passive tracer
subject to the motion of an ergodic Markovian flow of...
We discuss the existence problem of constant Chern scalar
curvature metrics on a compact complex manifold. We prove a priori
estimates for these metrics conditional on an upper bound on the
entropy, extending a recent result by Chen-Cheng in the...
In this three-part lecture series, we will present a series of
works by Bedrossian, Blumenthal and Punshon-Smith on the chaotic
mixing and enhanced dissipation properties of a passive tracer
subject to the motion of an ergodic Markovian flow of...
I will present a recent result jointly with Francisco Gancedo
(Universidad de Sevilla) and Huy Q. Nguyen (University of
Maryland), in which we obtained the global well-posedness for the
2D one-phase Muskat problem with arbitrary large Lipschitz...
In this three-part lecture series, we will present a series of
works by Bedrossian, Blumenthal and Punshon-Smith on the chaotic
mixing and enhanced dissipation properties of a passive tracer
subject to the motion of an ergodic Markovian flow of...
The non-resistive electron magnetohydrodynamics (MHD) has some
peculiar connection with the Euler equation. Some one-dimensional
reduced models are suggested as an attempt to build intuition
toward understanding the nonlinear structure and dynamics...
