Delayed blow-up by transport noise

具有输运噪声的三维纳维-斯托克斯方程不存在爆破现象

On the absence of blow-up in the 3D Navier-Stokes equations with transport noise

研究具有大初始数据的三维纳维-斯托克斯方程解的全局时间光滑性问题，通过适当的输运噪声驱动，证明方程以高概率有全局时间光滑解，且正则化效应在亚临界函数空间大球内初始数据上一致成立。

Noise Prevents Singularities in Linear Transport Equations

A stochastic linear transport equation with multiplicative noise is considered and the question of no-blow-up is investigated. The drift is assumed only integrable to a certain power. Opposite to the deterministic case where smooth initial conditions may develop discontinuities, we prove that a certain Sobolev degree of regularity is maintained, which implies Hölder continuity of solutions. The proof is based on a careful analysis of the associated stochastic flow of characteristics.

随机Córdoba--Córdoba--Fontelos方程中的伪微分噪声与非局部奇异性形成

Pseudo-differential noise and nonlocal singularity formation in the stochastic Córdoba--Córdoba--Fontelos equation

该研究针对乘性Stratonovich噪声驱动的随机Córdoba--Córdoba--Fontelos方程，建立了极大经典解的局部时间理论，证明有限时间爆破的相关性质并确定了爆破速率，为该类方程的奇异性研究提供了理论支撑。

Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations

By using a regularity approximation argument, the global existence and uniqueness are derived for a class of nonlinear SPDEs depending on both the whole history and the distribution under strong enough noise. As applications, the global existence and uniqueness are proved for distribution-path dependent stochastic transport type equations, which are arising from stochastic fluid mechanics with forces depending on the history and the environment. In particular, the distribution-path dependent stochastic Camassa--Holm equation with or without Coriolis effect has a unique global solution when the…

带输运噪声和临界超线性扩散的反应扩散方程：局部适定性与正性

Reaction-diffusion equations with transport noise and critical superlinear diffusion: local well-posedness and positivity

本文研究带输运噪声和临界超线性扩散的随机反应扩散方程，利用 $L^p(L^q)$-理论、极大正则性估计和精细爆破准则建立局部适定性、高阶正则性及正性，为一大类反应扩散系统的全局适定性提供通用工具。

Leray投影传输噪声的闭估计与随机Euler方程的强解

Closed Estimates of Leray Projected Transport Noise and Strong Solutions of the Stochastic Euler Equations

本文研究了三维环面上受传输或传输-拉伸Stratonovich噪声扰动的不可压缩Euler和Navier-Stokes方程，通过控制Leray投影破坏导数抵消带来的影响，首次证明了相应随机Euler方程局部强解的存在性及光滑解在爆破前的存在性。

A local-in-time theory for singular SDEs with applications to fluid models with transport noise

In this paper, we establish a local theory, i.e., existence, uniqueness and blow-up criterion, for a general family of singular SDEs in some Hilbert space. The key requirement is an approximation property that allows us to embed the singular drift and diffusion mappings into a hierarchy of regular mappings that are invariant with respect to the Hilbert space and enjoy a cancellation property. Various nonlinear models in fluid dynamics with transport noise belong to this type of singular SDEs. With a cancellation estimate for generalized Lie derivative operators, we can construct such regular a…

具有输运噪声的随机 Navier-Stokes 方程的增强耗散

Enhanced dissipation for stochastic Navier-Stokes equations with transport noise

本文研究输运噪声对随机 Navier-Stokes 方程的正则化作用，在二维速度形式中证明增强耗散，并在三维涡量形式中通过定量噪声参数选择以接近 1 的概率抑制爆破、获得全局解。

带传输噪声的SPDEs尺度极限的定量收敛速度

Quantitative convergence rates for scaling limit of SPDEs with transport noise

本文研究了带传输噪声的随机二维无粘流体方程向确定性粘性方程的尺度极限，结合分析与概率方法给出了定量收敛速度，并将该思想应用于随机Keller-Segel模型以控制爆破概率及增强耗散。