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Remark on Mild Solution to the 3D Incompressible Micropolar System in Fourier-Herz Framework
Yao; NIE; Xiao; Xin; ZHENG School; of; Mathematics; and; Systems; Science; Beihang; University; Beijing; 100191; P.R.China
- micropolar
- system
- space
- norm
- inflation
摘要：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 FB1,q^-1(q>2) is arbitrarily small, however, the couple(u0,ω0) produces a solution which is arbitrarily large in FB1,q^-1 after an arbitrarily short time. This implies the system is ill-posed in the sense of "norm inflation" as q>2.
- micropolar
- system
- space
- norm
- inflation
摘要：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 FB1,q^-1(q>2) is arbitrarily small, however, the couple(u0,ω0) produces a solution which is arbitrarily large in FB1,q^-1 after an arbitrarily short time. This implies the system is ill-posed in the sense of "norm inflation" as q>2.
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