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.
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Accepted: July 15, 2000
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Neustupa, J., Pokorný, M. An Interior Regularity Criterion for an Axially Symmetric Suitable Weak Solution to the Navier—Stokes Equations. J. math. fluid mech. 2, 381–399 (2000). https://doi.org/10.1007/PL00000960
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DOI: https://doi.org/10.1007/PL00000960