Stability of Navier–Stokes System with Singular External Force in Fourier–Herz Space

We prove the asymptotic properties of the solutions to the 3D Navier–Stokes system with singular external force, by making use of Fourier localization method, the Littlewood–Paley theory and some subtle estimates in Fourier–Herz space. The main idea of the proof is motivated by that of Cannone et al. [J. Differential Equations, 314, 316–339(2022)]. We deal either with the nonstationary problem or with the stationary problem where solution may be singular due to singular external force. In this paper, the Fourier–Herz space includes the function space of pseudomeasure type used in Cannone et al. [J. Differential Equations, 314, 316–339(2022)]