Abstract
ABSTRACT In this paper, the local existence and uniqueness of weak solutions to a d-dimensional non-resistive MHD equations in homogeneous Besov spaces are studied. Specifically we obtain the local existence of a weak solution ( u , b ) of the non-resistive MHD equations for the initial data u 0 ∈ B ˙ p , 1 d p − 1 ( R d ) and b 0 ∈ B ˙ p , 1 d p ( R d ) with 1 ≤ p ≤ ∞ , and the uniqueness of the weak solution when 1 ≤ p ≤ 2 d . Compared with the previous results for the non-resistive MHD equations, in the local existence part, the range of p extends to 1 ≤ p ≤ ∞ from 1 ≤ p ≤ 2 d , but the uniqueness of the solution requires 1 ≤ p ≤ 2 d yet.
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