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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
On the Damped Euler--Monge--Ampère equations with Radial Symmetry: Critical Thresholds and Large-Time Behavior
Kunhui Luan
We investigate the global well-posedness and large-time dynamics of the pressureless Euler--Monge--Ampère (EMA) system with velocity damping in multidimensions, subject to radiall…
math.AP2025
On the Euler-Poisson equations with variable background states and nonlocal velocity alignment
Kunhui Luan, Changhui Tan, Qiyu Wu
We study the 1D pressureless Euler-Poisson equations with variable background states and nonlocal velocity alignment. Our main focus is the phenomenon of critical thresholds, where…