AI 中文总结
该研究针对带乘性噪声的二维随机次黏滞Navier-Stokes方程，利用随机极大正则性与涡度方程的L^q能量估计，证明了其整体适定性。
AI 中文摘要
我们在环面上研究具有耗散项(-Δ)^γ（γ∈(1/2,1]）和乘性噪声的随机次黏滞Navier-Stokes方程。基于线性方程的随机极大正则性结果，我们建立了该问题在任意维数下、初值属于一定范围的尺度临界Besov空间时的局部适定性。借助涡度方程的L^q能量估计，我们还证明了带有线性乘性噪声的二维随机次黏滞Navier-Stokes方程的整体适定性。
英文摘要
We study stochastic hypoviscous Navier--Stokes equations on the torus with dissipation $(-Δ)^γ$ for $γ\in (\frac{1}{2},1]$ and multiplicative noise. Relying on stochastic maximal regularity results for the linear equation, we establish local well-posedness for this problem in arbitrary dimensions with initial data in a range of scaling-critical Besov spaces. With the aid of $L^q$-energy estimates for the vorticity equation, we also prove global well-posedness of the stochastic hypoviscous Navier--Stokes equation in 2D with linear multiplicative noise.
CommentsSubmitted to the Oberwolfach Seminar 'Stochastic Partial Differential Equations in Critical Spaces' organised by Antonio Agresti and Mark Veraar
