Muliti-scale regularity of axisymmetric Navier-Stokes equations

2018/02/25 by Daoyuan Fang, Hui Chen, Fang, Daoyuan +3
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1802.08956

Abstract

By applying the delicate a priori estimates for the equations of (Φ,Γ), which is introduced in the previous work, we obtain some multi-scale regularity criteria of the swirl component u^θ for the 3D axisymmetric Navier-Stokes equations. In particularly, the solution u can be continued beyond the time T, provided that u^θ satiesfies u^θ ∈ L^p_TL^q_vvL^q_h,w_h,~~(2)/(p)+\frac1q_v+\frac2q_h≤ 1, ~2

Citations

• Liouville theorems for the Navier–Stokes equations and applications

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