Wavelets and the well-posedness of incompressible magneto-hydrodynamic equations in Besov type Q-space

In this paper, we introduce a class of Besov type Q-spaces Ḃp,pγ1,γ2(Rn) to study the well-posedness of the fractional magneto-hydrodynamic (FMHD) equations. Applying wavelets and multi-resolution analysis, we obtain the boundedness of a semigroup operator from Ḃp,pγ1,γ2(Rn) to some tent spaces Bp,m,m′γ1,γ2. As an application, we prove the global well-posedness of equations (FMHD) with data in Ḃp,pγ1,γ2(Rn). Compared with the method of Fourier transform, the advantage of our method can be applied to the well-posedness with initial data in Ḃp,pγ1,γ2(Rn), where p≠2.