We prove asymptotic stability of shear flows close to the planar Couette flow in the 2D
inviscid Euler equations on T× R. That is, given an initial perturbation of the Couette flow …

The dynamics of forming patterns in biological, chemical, and physical systems has received
considerable attention over recent years (see eg Cross and Hohenberg, 1993). In the …

In N-body systems with long-range interactions mean-field effects dominate over binary
interactions (collisions), so that relaxation to thermal equilibrium occurs on time scales that …

In this expository note, we discuss our recent work on the nonlinear asymptotic stability of
shear flows in the 2D Euler equations of ideal, incompressible flow. In that work, it is proved …

We discuss results on the dynamics of thermalization for a model with Gaussian interactions
between two classical many-body systems trapped in external harmonic potentials. Previous …

Stability properties and mode signature for equilibria of a model of electron temperature
gradient (ETG) driven turbulence are investigated by Hamiltonian techniques. After deriving …

This chapter describes Hamiltonian bifurcations in the context of noncanonical Hamiltonian
matter model. First, a large class of 1+ 1 Hamiltonian multifluid models is considered. These …

We discuss the scaling of the interaction energy with particle numbers for a harmonically
trapped two-species mixture at thermal equilibrium experiencing interactions of arbitrary …

Bifurcations of unstable modes from the continuous spectrum underlie pattern formation in a
wide variety of physical systems that can be described by Hamiltonian 2+ 1 field theories …