Global Well-posedness for the Non-viscous MHD Equations with Magnetic Diffusion in Critical Besov Spaces

In this paper, we mainly investigate the Cauchy problem of non-viscous MHD equations with magnetic diffusion. We first establish local well-posedness (existence, uniqueness and continuous dependence) initial data (u0, b0) in critical Besov spaces \(B_{p,1}^{{d \over p} + 1} \times B_{p,1}^{{d p}}\) 1 ≤ p ∞, give a lifespan T solution which depends on norm Littlewood—Paley decomposition (profile) data. Then, prove global existence spaces. particular, results also hold Sobolev space \(C\left( {[0,\infty } \right);{H^s}\left. {\left( {{\mathbb{S}^2}} \right)} \right) \left( {C\left( \right);{H^{s - 1}}\left. \cap {L^2}\left( {{\mathbb{S}^2}}\right)} \right)\) s> 2, when satisfies \(\int_{{\mathbb{S}^2}} {{b_0}dx} = 0\) \({\left\| {{u_0}} \right\|_{B_{\infty ,1}^1\left( \right)}} {\left\| {{b_0}} ,1}^0\left( \le \epsilon\). It’s worth noting that our imply some large low regularity for existence.