Regularity criterion for 3D Navier-Stokes Equations in Besov spaces

2012/10/14 by Daoyuan Fang, Fang, Daoyuan, Chenyin Qian +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1210.3857

openalex publication_date 2012/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Several regularity criterions of Leray-Hopf weak solutions u to the 3D Navier-Stokes equations are obtained. The results show that a weak solution u becomes regular if the gradient of velocity component ∇_hu (or ∇u₃) satisfies the additional conditions in the class of L^q(0,T; B_p,r^s(ℝ³)), where ∇_h=(∂_x₁,∂_x₂) is the horizontal gradient operator. Besides, we also consider the anisotropic regularity criterion for the weak solution of Navier-Stokes equations in ℝ³. Finally, we also get a further regularity criterion, when give the sufficient condition on ∂₃u₃.

Citations

• The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations

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