Existence and Uniqueness of Local Weak Solution of D-Dimensional Fractional Micropolar Rayleigh-Bénard Convection System Without Thermal Diffusion in Besov Space

This paper studies the existence and uniqueness of local weak solutions to the d-dimensional ( $d\ge 2$ ) fractional micropolar Rayleigh-Bénard convection system without thermal diffusion. When the fractional dissipation index $1\leq \alpha <1+\frac{d}{4}$ , any initial data $(u_{0},\omega _{0})\in B_{2,1}^{1+\frac{d}{2}-2\alpha}(\mathbb{R}^{d})$ and $\theta _{0}\in B_{2,1}^{1+\frac{d}{2}-\alpha}(\mathbb{R}^{d})$ yield a local unique weak solution.