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三维微极Rayleigh-Bénard对流方程在Triebel-Lizorkin空间中的正则性准则
Regularity Criteria for the Three-Dimensional Micropolar Rayleigh-Bénard Convection Equations in Triebel-Lizorkin Spaces

DOI: 10.12677/pm.2026.162046, PP. 173-184

Keywords: Rayleigh-Bénard对流方程,正则性准则,压力,Triebel-Lizorkin空间
Rayleigh-Bénard Convection Equation
, Regularity Criteria, Pressure, Triebel-Lizorkins Space

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Abstract:

本文考虑三维微极Rayleigh-Bénard对流方程,设 ( u,ω,θ )( t,x ) 是方程在 ( 0,T ) 上的Leray-Hopf弱解。证明当压力满足 q> 12 5 , ∫ 0 T ‖ π ‖ F ˙ q, 10q 5q+6 ( ? 3 ) 0 10q 5q?6 dτ<∞ ,或者压力的梯度满足 12 11 <q<4 , ∫ 0 T ‖ ?π ‖

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