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On the regularity criterion of axisymmetric weak solutions to the 3D Navier–Stokes equations

✍ Scribed by Sadek Gala

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
224 KB
Volume
74
Category
Article
ISSN
0362-546X

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✦ Synopsis

In this paper, we consider the regularity criterion of axisymmetric weak solutions to the Navier-Stokes equations in R 3 . Let u be an axisymmetric weak solution in R 3 × (0, T ), w = curl u, and w θ be the azimuthal component of w in the cylindrical coordinates. It is proved that u becomes a regular solution if w θ ∈ L 2 2-s (0, T ; . M 2, 3 s ), where . M 2, 3 s is the critical Morrey-Campanato space.

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