Regularity of 3D axisymmetric Navier-Stokes equations

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 $(\frac{{\omega }^r}{r},\frac{{\omega }^{\theta }}{r})$, we get several Prodi-Serrin type regularity criteria based on the angular velocity, $u^{\theta }$. Moreover, we obtain the global well-posedness result if the initial angular velocity $u_0^{\theta }$ is appropriate small in the critical space $L^3({\mathbb{R}}^3)$. Furthermore, we also get several Prodi-Serrin type regularity criteria based on one component of the solutions, say ${\omega }^3$ or $u^3$.

References in corpus (4)

• Lower bounds on the blow-up rate of the axisymmetric Navier-Stokes equations II
• Some new regularity criteria for the 3D Navier-Stokes Equations
• Several almost critical regularity conditions based on one component of the solutions for 3D N-S Equations
• Global smooth axisymmetric solutions of 3-D Inhomogenenous incompressible Navier-Stokes system

Cited by in corpus (3)

• Criticality of the Axially Symmetric Navier-Stokes Equations
• Regularity Criterion to the axially symmetric Navier-Stokes Equations
• Global regularity for a family of 3D models of the axisymmetric Navier-Stokes equations