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Time fractional stochastic Navier-Stokes equations driven by fractional Brownian motion

Authors

  • Caibin Zeng School of Mathematics, South China University of Technology, Guangzhou 510640, P.R. China

Keywords:

Navier-Stokes equation, fractional Brownian motion, fractional differential equations, Mittag-Leffler functions, mild solution

Abstract

A two-dimensional time fractional stochastic incompressible Navier-Stokes equations driven by fractional Brownian motion is studied with the Hurst parameter \(H\in(1/2,1)\) and time fractional differential operator of order \(\alpha\in(0,1)\) under the Dirichlet boundary condition. Without the requirement of compact parameters, the existence and regularity of the nonlocal stochastic convolution are obtained by combining the estimate on the spectrum of the Stokes operator under a square domain, an upper bound of a class of the generalized Mittag-Leffler functions, and the fractional calculus technique. Moreover, sufficient conditions are provided to ensure the local and global existence and uniqueness of mild solutions, as well as the square integrability and continuity of the solution's paths.

Additional Files

Published

08-09-2023

How to Cite

Zeng, C. (2023). Time fractional stochastic Navier-Stokes equations driven by fractional Brownian motion. Letters on Applied and Pure Mathematics, 1(2), 1–20. Retrieved from https://lapmjournal.com/index.php/lapm/article/view/lapm.20231214

Issue

Section

Research Article