New approach in the Besov space to the existence and uniqueness of solutions of the D-dimensional fractional magnetic Bénard system without thermal diffusion

2024/09/08 by Rahmani, Anis, Mennouni, Abdelaziz
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.17151

Abstract

This work investigates the existence and uniqueness of local weak solutions for the d-dimensional (d ≥ 2) fractional magnetic Bénard system without thermal diffusion, integrating the Bénard equation and MHD system. For κ= 0 and 1 ≤ α=β< 1 + \dfracd4, we establish that any starting conditions (u₀,B₀)∈ B_2,1^{1+(d)/(2)-2α}(ℝ^d) and θ₀∈ B_2,1^1+(d)/(2)-α(ℝ^d).

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