Jiang-Wei Zhang

Enhanced Dissipation under Variable Growth: Stochastic $p(x)$-Laplace Equations with Transport Noise

We study dissipation enhancement for stochastic $p(x)$-Laplace equations with divergence-free transport noise on $\mathbb T^d$, $d\ge2$. Under log-H\"older continuity and degenerate subcritical growth, we establish global variational well-posedness and an exact energy identity. For every prescribed positive coefficient...

Invariant Measures and Ergodicity of Stochastic p(x)-Laplace Equations with Spatially Variable Exponents Driven by Nonlinear Noise

Random Pullback Attractors and Numerical Approximation for Nonlocal Lattice Delay Equations Driven by Rough Noise

We investigate the pathwise asymptotic dynamics of a nonlocal lattice equation with fixed delay on $\ell^2(\mathbb Z)$ driven by an infinite-dimensional stationary weakly geometric rough path. Using a rough-flow Doss-Sussmann transformation and the method of steps, we establish global well-posedness in the controlled-p...

Unique Ergodicity for Strongly Damped Stochastic Wave Equations under Finite-Rank Pure-Jump L\'{e}vy Forcing

We study a strongly damped stochastic wave equation on the three-dimensional torus driven by finite-rank pure-jump L\'{e}vy noise obtained from subordinated Brownian motion. Lyapunov estimates and an asymptotic compactness decomposition yield invariant measures, and a small-noise event gives weak irreducibility. To pro...

Commutator Estimates Uniform in the Screening Parameter and Mean-Field Limits for Yukawa Interactions

We study quantitative mean-field limits for classical particles with Yukawa (screened Coulomb) interactions in every fixed dimension $d\ge2$, uniformly as the screening parameter $\kappa$ tends to zero. Our main result is a first-order commutator estimate in the natural Yukawa modulated energy, with an additive error o...

Pullback Measure Attractors, Zero-Noise Limits, and Moderate Deviations for 2D Stochastic Primitive Equations with Multiplicative L\'{e}vy Noise

We study the long-term distributional dynamics and small-noise asymptotics of two-dimensional nonautonomous stochastic primitive equations driven by Gaussian and multiplicative L\'evy noise, together with moderate deviations for the purely jump model. For sufficiently small noise, uniform moment bounds and an exponenti...

Quantitative mean-field limits for repulsive Coulomb flows at bounded density and Riesz weak--strong stability

We establish quantitative mean-field convergence and propagation of chaos for repulsive Coulomb gradient flows at the bounded-density regularity of the limiting equation. The argument couples the dissipative modulated-energy identity with the normalized quadratic transport cost of the full $N$-particle law. The remaini...