Well-Posedness for Stochastic Fractional Navier–Stokes Equation in the Critical Fourier–Besov Space

Xiuwei Yin (), Jiang-Lun Wu () and Guangjun Shen ()
Additional contact information
Xiuwei Yin: Anhui Normal University
Jiang-Lun Wu: Swansea University
Guangjun Shen: Anhui Normal University

Journal of Theoretical Probability, 2022, vol. 35, issue 4, 2940-2959

Abstract: Abstract The well-posedness of stochastic Navier–Stokes equations with various noises is a hot topic in the area of stochastic partial differential equations. Recently, the consideration of stochastic Navier–Stokes equations involving fractional Laplacian has received more and more attention. Due to the scaling-invariant property of the fractional stochastic equations concerned, it is natural and also very important to study the well-posedness of stochastic fractional Navier–Stokes equations in the associated critical Fourier–Besov spaces. In this paper, we are concerned with the three-dimensional stochastic fractional Navier–Stokes equation driven by multiplicative noise. We aim to establish the well-posedness of solutions of the concerned equation. To this end, by utilising the Fourier localisation technique, we first establish the local existence and uniqueness of the solutions in the critical Fourier–Besov space $$\dot{\mathcal {B}}^{4-2\alpha -\frac{3}{p}}_{p,r}$$ B ˙ p , r 4 - 2 α - 3 p . Then, under the condition that the initial date is sufficiently small, we show the global existence of the solutions in the probabilistic sense.

Keywords: Stochastic fractional Navier–Stokes equation; Fourier–Besov spaces; Strong solutions; 60H15; 76D05; 42B37 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-021-01152-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:35:y:2022:i:4:d:10.1007_s10959-021-01152-y

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-021-01152-y

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().