Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 74, pp. 1-10.

Title: Well-posedness of solutions for the 2D stochastic quasi-geostrophic equation in critical Fourier-Besov-Morrey spaces

Authors: Hassan Khaider (Sultan Moulay Slimane Univ., Beni Mellal, Morocco)
         Achraf Azanzal (Hassan First Univ., Settat, Morocco)
         Abderrahmane Raji (Sultan Moulay Slimane Univ., Beni Mellal, Morocco)

Abstract: 
In this article, we apply the Ito integral to obtain the global 
solutions for stochastic quasi-geostrophic equations in 
Fourier-Besov-Morrey spaces. For comparison we also give the 
corresponding results of the deterministic quasi-geostrophic equations. 
We assume  the initial data  is $F_0$ measurable and
the right-hand side is a random function in a Morrey space,
to obtain the well posedness of stochastic quasi-geostrophic equations.

Submitted June 26, 2024. Published November 20, 2024.
Math Subject Classifications: 35Q35, 42B37, 35Q85, 35R60.
Key Words: Ito integral; stochastic quasi-geostrophic equations; Fourier-Besov-Morrey spaces; partial differential equations.