New approach in the Besov space to the existence and uniqueness of solutions of the D-dimensional fractional magnetic Bénard system without thermal diffusion
This work investigates the existence and uniqueness of local weak solutions for the d-dimensional $(d \geq 2)$ fractional magnetic Bénard system without thermal diffusion, integrating the Bénard equation and MHD system. For $κ= 0$ and $1 \leq α=β< 1 + \dfrac{d}{4}$, we establish that any starting conditions $(u_{0},B_{0})\in B_{2,1}^{1+\frac{d}{2}-2α}(\mathbb{R}^{d})$ and $θ_{0}\in B_{2,1}^{1+\frac{d}{2}-α}(\mathbb{R}^{d})$.
math.AP↗