Kyle L. Liss

activity

20182026

most citedOn the Sobolev stability threshold of 3D Couette flow in a homogeneous magnetic field

1 citations · 4 across the 10 of their papers we have counts for

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7 papers · 1 filter

math.AP2026

Uniform-in-diffusivity mixing by shear flows: stochastic and dynamical perspectives

Kyle L. Liss, Kunhui Luan

We study passive scalar mixing by parallel shear flows in the presence of weak molecular diffusion. We recover the sharp uniform-in-diffusivity mixing rate for shear flows with fin…

math.AP2026

The Batchelor spectrum for a deterministically driven passive scalar

Kyle L. Liss, Jonathan C. Mattingly

We study the long-time behavior of a passive scalar transported by an incompressible flow in the presence of smooth, deterministic forcing. For a specific spatially Lipschitz and t…

math.AP2024

A pathwise approach to the enhanced dissipation of passive scalars advected by shear flows

Victor Gardner, Kyle L. Liss, Jonathan C. Mattingly

We develop a framework for studying the enhanced dissipation of passive scalars advected by shear flows based on analyzing the particle trajectories of the stochastic differential…

math.AP2023

Norm Growth, Non-uniqueness, and Anomalous Dissipation in Passive Scalars

Tarek M. Elgindi, Kyle Liss

We construct a divergence-free velocity field $u : [0, T] \times T^{2} \to R^{2}$ satisfying $u \in C^{\infty} ([0, T]; C^{α} (T^{2})) \forall α \in [0, 1)$ such th…

math.AP2023★ 1 cited

Optimal enhanced dissipation and mixing for a time-periodic, Lipschitz velocity field on $T^{2}$

Tarek M. Elgindi, Kyle Liss, Jonathan C. Mattingly

We consider the advection-diffusion equation on $T^{2}$ with a Lipschitz and time-periodic velocity field that alternates between two piecewise linear shear flows. We prove…

math.AP2020★ 1 cited

Quantitative spectral gaps and uniform lower bounds in the small noise limit for Markov semigroups generated by hypoelliptic stochastic differential equations

Jacob Bedrossian, Kyle Liss

We study the convergence rate to equilibrium for a family of Markov semigroups ${P_{t}^{ε}}_{ε > 0}$ generated by a class of hypoelliptic stochastic differential equations o…

math.AP2018★ 1 cited

On the Sobolev stability threshold of 3D Couette flow in a homogeneous magnetic field

Kyle Liss

We study the stability of the Couette flow $(y, 0, 0)^{T}$ in the 3D incompressible magnetohydrodynamic (MHD) equations for a conducting fluid on $\mathbb{T} \times \mathbb{R} \times \…