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 ≥ 2 ) fractional micropolar Rayleigh-Bénard convection system without thermal diffusion. When the fractional dissipation index 1 ≤ α < 1 + d 4 , any initial data ( u 0 , ω 0 ) ∈ B 2 , 1 1 + d 2 − 2 α ( R d ) and θ 0 ∈ B 2 , 1 1 + d 2 − α ( R d ) yield a local unique weak solution.