arXiv subjects

Shuaijie Jiao

Publications and source records attributed to Shuaijie Jiao.

4 recordsLinked to original sources

arXiv2026

Delayed Blow-up in 3D Fluids via Pseudo-transport Noise

We establish scaling limit results for fluid dynamics equations driven by pseudo-transport noise. The behaviour of noise at small scales is governed by a parameter a. This extends previous results by Flandoli and Luo (2020) and Galeati (2020), which correspond to a=0 in our setting. Depending on the value of a, we prove that the noise delays the potential blow-up of both the 3D Euler and Navier-Stokes (NS) equations with high probability.

math.PR↗

arXiv2025

Strong Uniqueness by Kraichnan Transport Noise for the 2D Boussinesq Equations with Zero Viscosity

We investigate the inviscid 2D Boussinesq equations driven by rough transport noise of Kraichnan type with regularity index $α\in (0,1/2)$. For all $1<p<\infty$, we establish the existence and uniqueness of probabilistic strong solutions for all $L^p$ initial vorticity and $L^2$ initial temperature, under the parameter constraint $0<α< 1-1/(p\wedge 2)$. The key ingredient is the anomalous regularity due to the noise proven by Coghi and Maurelli \cite{CogMau} who dealt with stochastic 2D Euler equations. Combining techniques from analysis and probability, we demonstrate how the additional regularity from noise compensates the singularity due to the nonlinear parts and coupled terms.

math.PR↗

arXiv2024

On the pathwise uniqueness of stochastic 2D Euler equations with Kraichnan noise and $L^p$-data

In the recent work [arXiv:2308.03216], Coghi and Maurelli proved pathwise uniqueness of solutions to the vorticity form of stochastic 2D Euler equation, with Kraichnan transport noise and initial data in $L^1\cap L^p$ for $p>3/2$. The aim of this note is to remove the constraint on $p$, showing that pathwise uniqueness holds for all $L^1\cap L^p$ initial data with arbitrary $p>1$.

math.PR↗

arXiv2024

Well-posedness of stochastic mSQG equations with Kraichnan noise and $L^p$ data

We consider stochastic mSQG (modified Surface Quasi-Geostrophic) equations with multiplicative transport noise of Kraichnan type, and $L^p$-initial conditions. Inspired by the recent work of Coghi and Maurelli [arXiv:2308.03216], we show weak existence and pathwise uniqueness of solutions to the equations for suitable choices of parameters in the nonlinearity, the noise and the integrability of initial data.

math.PR↗