Remarks on the global smooth solution of the 3D generalized magneto-micropolar equations

This paper is concerned with the global smooth solution of the 3D generalized magneto-micropolar equations. When the velocity dissipation is logarithmically hyperdissipative and the magnetic diffusion is fractional Laplacian, based on some new observations on the nonlinear structure for the magneto-micropolar equations, it is examined the system has a unique global smooth solution (u,w,b)is an element of C([0,T];Hs(Double-struck capital R3))$$ \left(u,w,b\right)\in C\left(\left[0,T\right];{H} circumflex s\left({\mathrm{\mathbb{R}}} circumflex 3\right)\right) $$.

Automated summary

This paper deals with the global smooth solution of the 3D generalized magneto-micropolar equations. By making new observations on the nonlinear structure of the magneto-micropolar equations, it is shown that the system has a unique global smooth solution when the velocity dissipation is logarithmically hyperdissipative and the magnetic diffusion is fractional Laplacian.