Kyle L Liss

Journal Article Archive for Rational Mechanics and Analysis · December 1, 2024 We construct a divergence-free velocity field u:[0,T]×T2→R2 satisfying (Formula presented.) such that the corresponding drift-diffusion equation exhibits anomalous dissipation for all smooth initial data. We also show that, given any α0<1, the flow can be ... Full text Cite

Stationary measures for stochastic differential equations with degenerate damping

Journal Article Probability Theory and Related Fields · June 1, 2024 A variety of physical phenomena involve the nonlinear transfer of energy from weakly damped modes subjected to external forcing to other modes which are more heavily damped. In this work we explore this in (finite-dimensional) stochastic differential equat ... Full text Cite

QUANTITATIVE SPECTRAL GAPS FOR HYPOELLIPTIC STOCHASTIC DIFFERENTIAL EQUATIONS WITH SMALL NOISE

Journal Article Probability and Mathematical Physics · January 1, 2021 We study the convergence rate to equilibrium for a family of Markov semigroups {Pɛt}ɛ>0 generated by a class of hypoelliptic stochastic differential equations on Rd, including Galerkin truncations of the incompressible Navier–Stokes equations, Lorenz-96, a ... Full text Cite

On the Sobolev Stability Threshold of 3D Couette Flow in a Uniform Magnetic Field

Journal Article Communications in Mathematical Physics · July 1, 2020 We study the stability of the Couette flow (y, 0 , 0) T in the presence of a uniform magnetic field α(σ, 0 , 1) on T× R× T using the 3D incompressible magnetohydrodynamics (MHD) equations. We consider the inviscid, ideal conductor limit Re- 1, Rm-1≪1 and p ... Full text Cite