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

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]. For more information see https://ejde.math.txstate.edu/Volumes/2025/35/abstr.html