Stochastic 3D Leray-α model with fractional dissipation
Stochastic 3D Leray-α model with fractional dissipation
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DOI：
10.1007/s11425-021-2039-8
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发表时间：
2023-08
期刊：
影响因子：
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通讯作者：
Shihu Li;W. Liu;Yingchao Xie
中科院分区：
文献类型：
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作者：
Shihu Li;W. Liu;Yingchao Xie
本文建立了乘性噪声驱动的具有一般分数耗散的随机三维Leray-α模型的整体适定性.该模型是三维随机Navier-Stokes方程，通过非线性项中的θ 1阶光滑核和θ2-分数Laplacian正则化.在θ1 ≥ 0和θ2> 0的情形下，证明了强解的整体存在唯一性.主要结果不仅涵盖了确定性情形下已有的许多工作，而且作为特例推广了随机模型如随机高粘性Navier-Stokes方程和经典随机三维Leray-α模型的一些已知结果.
In this paper, we establish the global well-posedness of the stochastic 3D Leray-αmodel with general fractional dissipation driven by multiplicative noise. This model is the stochastic 3D Navier-Stokes equations regularized through a smoothing kernel of orderθ1in the nonlinear term and theθ2-fractional Laplacian. In the case ofθ1⩾ 0 andθ2> 0 with, we prove the global existence and uniqueness of strong solutions. The main results not only cover many existing works in the deterministic cases, but also generalize some known results of stochastic models such as the stochastic hyperviscous Navier-Stokes equations and classical stochastic 3D Leray-αmodel as the special cases.