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

In this paper, we introduce a class of Besov type Q -spaces B ̇ p , p γ 1 , γ 2 ( R n ) 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 B ̇ p , p γ 1 , γ 2 ( R n ) to some tent spaces B p , m , m ′ γ 1 , γ 2 . As an application, we prove the global well-posedness of equations (FMHD) with data in B ̇ p , p γ 1 , γ 2 ( R n ) . Compared with the method of Fourier transform, the advantage of our method can be applied to the well-posedness with initial data in B ̇ p , p γ 1 , γ 2 ( R n ) , where p ≠ 2 .