Regularity Criterion Involving the Middle Eigenvalue of the Strain Tensor to the 3D Micropolar Bénard Equations

ABSTRACT In this paper, by using energy methods and the Littlewood‐Paley decomposition theory, we obtain regularity criteria for the strong solution of the 3D micropolar Bénard equations, which only involves the positive part of the middle eigenvalue of the strain matrix in two classes of Besov spaces. Specifically, the criteria are .