2021/05/07 by Weikui Ye, Zhaoyang Yin, Ye, Weikui +1 · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2105.03124
openalex publication_date 2021/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we mainly investigate the Cauchy problem of the non-viscous MHD equations with magnetic diffusion. We first establish the local well-posedness (existence,~uniqueness and continuous dependence) with initial data (u0,b0) in critical Besov spaces B(d)/(p)+1p,1×B(d)/(p)p,1 with 1≤ p≤∞, 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,∞); Hs(\mathbbS2))× (C([0,∞);Hs-1(\mathbbS2))∩ L2([0,∞);Hs(\mathbbS2))) with s>2, when the initial data satisfies ∫_\mathbbS2b0dx=0 and ‖u0‖_B1∞,1(\mathbbS2)+‖b0‖_B0∞,1(\mathbbS2)≤ ε. 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 \citeweishen.