Regularity of 3D axisymmetric Navier-Stokes equations

2015/05/05 by Hui Chen, Chen, Hui, Daoyuan Fang +3
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1505.00905

Abstract

In this paper, we study the three-dimensional axisymmetric Navier-Stokes system with nonzero swirl. By establishing a new key inequality for the pair (\fracω^rr,(ω^θ)/(r)), we get several Prodi-Serrin type regularity criteria based on the angular velocity, u^θ. Moreover, we obtain the global well-posedness result if the initial angular velocity u₀^θ is appropriate small in the critical space L³(\R³). Furthermore, we also get several Prodi-Serrin type regularity criteria based on one component of the solutions, say ω³ or u³.

Citations

• Liouville theorems for the Navier–Stokes equations and applications

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