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- W3162989690 abstract "In this paper, we mainly investigate the Cauchy problem of the resistive MHD equation without viscosity. We first establish the local well-posedness (existence,~uniqueness and continuous dependence) with initial data $(u_0,b_0)$ in critical Besov spaces $ {B}^{frac{d}{p}+1}_{p,1}times{B}^{frac{d}{p}}_{p,1}$ with $1leq pleqinfty$, and give a lifespan $T$ of the solution which depends on the norm of the Littlewood-Paley decomposition of the initial data. Then, we prove the global existence in critical Besov spaces. In particular, the results of global existence also hold in Sobolev space $ C([0,infty); {H}^{s}(mathbb{S}^2))times Big(C([0,infty);{H}^{s-1}(mathbb{S}^2))cap L^2big([0,infty);{H}^{s}(mathbb{S}^2)big)Big),~s>2$ when the initial data satisfies $int_{mathbb{S}^2}b_0dx=0$ and $|u_0|_{B^1_{infty,1}(mathbb{S}^2)}+|b_0|_{{B}^{1}_{2,1}(mathbb{S}^2)}leq epsilon$. It's worth noting that our results imply some large and low regularity initial data for the global existence, which improves considerably the recent results in cite{weishen}." @default.
- W3162989690 created "2021-05-24" @default.
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- W3162989690 date "2021-05-07" @default.
- W3162989690 modified "2023-09-27" @default.
- W3162989690 title "Global well-posedness for the resistive MHD equations in critical Besov spaces" @default.
- W3162989690 hasPublicationYear "2021" @default.
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