Analysis of time fractional and space nonlocal stochastic incompressible Navier–Stokes equation driven by white noise
Analysis of time fractional and space nonlocal stochastic incompressible Navier–Stokes equation driven by white noise
复制标题
白噪声驱动的时间分数和空间非局部随机不可压缩NavierStokes方程分析
DOI：
10.1016/j.camwa.2018.12.022
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发表时间：
2019
影响因子：
2.9
通讯作者：
Jiarui Liang
中科院分区：
文献类型：
--
作者：
Liyang Xu;Tianlong Shen;Xuejun Yang;Jiarui Liang
考虑白噪声驱动下的随机时空分数阶不可压缩Navier-Stokes方程。首先推导了非局部随机卷积的正则性。然后证明了该温和解的全局存在唯一性。最后，建立了白噪声驱动下随机时空分数阶不可压缩Navier-Stokes方程的Hölder连续性。最优Hölder连续性符合整阶时间不可压缩Navier-Stokes方程的结果。
In this paper, we consider the stochastic time-space fractional incompressible Navier–Stokes equation driven by white noise. We firstly derive the regularity of the nonlocal stochastic convolution. Then we prove the global existence and uniqueness of the mild solution. Finally, the Hölder continuity for the stochastic time-space fractional incompressible Navier–Stokes equation driven by white noise is established. The optimal Hölder continuity accords with the result of integer-order-time incompressible Navier–Stokes equation.