Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 35, pp. 1-33.

Title: Existence and uniqueness of global strong solutions for 3D fractional compressible systems

Authors: Mengqian Liu (Donghua Univ., Shanghai, China)
         Lei Niu   (Donghua Univ., Shanghai, China)
         Zhigang Wu (Donghua Univ., Shanghai, China)

Abstract:
In this article, we study the Cauchy problem for  3D fractional compressible 
isentropic generalized Navier-Stokes equations for viscous compressible 
fluid with one Levy diffusion process. 
We first obtain the existence and uniqueness of global strong solutions 
for small initial data by providing several commutators via the 
Littlewood-Paley theory. 
We then derive the L^2-decay rate for the highest derivative of the 
strong solution without decay loss by using a cancellation 
of a low-medium-frequency quantity. 
Our results improve those provided recently in [36].

Submitted June 30, 2024. Published April 06, 2025.
Math Subject Classifications: 35A09, 35B40;,35Q35.
Key Words: Fractional Navier-Stokes equations; global well-posedness;  uniqueness; optimal decay rate; Littlewood-Paley theory.