Remark on Mild Solution to the 3D Incompressible Micropolar System in Fourier-Herz Framework

This paper is devoted to investigating the existence and uniqueness of mild solution to the 3D incompressible micropolar fluid system in the Fourier-Herz framework. By taking advantage of microlocal analysis and the mutual effect in the same frequency range of convection term, we give a special initial data (u₀, ω₀) whose norm of FB˙1,q−1(q>2) is arbitrarily small, however, the couple (u₀, ω₀) produces a solution which is arbitrarily large in FB˙1,q−1 after an arbitrarily short time. This implies the system is ill-posed in the sense of “norm inflation” as q > 2.