Remarks on regularity criteria for axially symmetric weak solutions to the Navier-Stokes equations

Abstrakt

We examine the conditional regularity of the solutions to the Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axially symmetric. We show that if a radial or angular component of velocity satisfies a weighted Serrin condition, then the solution is regular.

Klíčová slova

• Navier-Stokes equations
• axial symmetry
• regularity criteria
• weighted spaces