An Interior Regularity Criterion for an Axially Symmetric Suitable Weak Solution to the Navier—Stokes Equations

Abstract.

We show that if v is an axially symmetric suitable weak solution to the Navier—Stokes equations (in the sense of L. Caffarelli, R. Kohn & L. Nirenberg — see [2]) such that either $v_{\rho}$ (the radial component of v) or $v_{\theta}$ (the tangential component of v) has a higher regularity than is the regularity following from the definition of a weak solution in a sub-domain D of the time-space cylinder Q _T then all components of v are regular in D.