Regularity criterion of axisymmetric weak solutions to the 3D Navier-Stokes equations |
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Authors: | Qionglei Chen |
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Institution: | a Institute of Applied Physics and Computational Mathematics, Beijing 100088, China b School of Mathematical Science, Peking University, Beijing 100871, China |
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Abstract: | We consider the regularity of axisymmetric weak solutions to the Navier-Stokes equations in R3. Let u be an axisymmetric weak solution in R3×(0,T), w=curlu, and wθ be the azimuthal component of w in the cylindrical coordinates. Chae-Lee D. Chae, J. Lee, On the regularity of axisymmetric solutions of the Navier-Stokes equations, Math. Z. 239 (2002) 645-671] proved the regularity of weak solutions under the condition wθ∈Lq(0,T;Lr), with , . We deal with the marginal case r=∞ which they excluded. It is proved that u becomes a regular solution if . |
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Keywords: | Navier-Stokes equation Regularity criterion Weak solutions Besov space |
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