Abstract: I will present a new approach to the isometric
embedding problem. The main new idea is to use the theory of
stochastic flows in combination with various possible gradient flow
structures. These ideas are motivated by the statistical...
Abstract: The purpose of this work is to perform a
mathematically rigorous study of Lagrangian chaos and "passive
scalar turbulence" in incompressible fluid mechanics. We study the
Lagrangian flow map associated to 2D Navier-Stokes and
hyper-viscous...
Abstract: We consider a class of dynamical systems described by
ordinary differential equations with an isolated singularity, where
the singularity is characterized by the lack of Lipschitz
continuity. Singularities are common in applications both...
Abstract: I will discuss the recent non-uniqueness result with
Vlad Vicol on the non-uniqueness of weak solutions to the
Navier-Stokes equations, as well as the follow up paper by myself,
Maria Colombo and Vicol. I hope to phrase the results within...
Abstract: I will discuss some preliminary work on using machine
learning
to produce turbulence models that can be used in large eddy
simulation.
I will discuss how better models can be constructed and in
general,
how one can use machine learning to...
Abstract: The confounding question of asymptotically high
Rayleigh number heat transport in Rayleigh-Bénard convection
modeled by the Boussineq approximation to the Navier-Stokes
equations is reviewed from viewpoints of theory (models of the
model)...
We are interested in moments of velocity increments and
derivatives, characterized by scaling exponents overline{(v(x + r)
− v(x))n} ∝ r^ζn and overline{(∂xvx)n} ∝ Re^ρn , respectively. In
high Reynolds number flows, the moments of different orders...
