Interior Regularity Criteria for Suitable Weak Solutions of the Navier-Stokes Equations

By Stephen Gustafson, Kyungkeun Kang, Tai-Peng Tsai. 2006

132 citations recorded by the source corpus.

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point z if either the scaled $${L^{p,q}_{x,t}}$$ -norm of the velocity with 3/p + 2/q ≤ 2, 1 ≤ q ≤ ∞, or the $${L^{p,q}_{x,t}}$$ -norm of the vorticity with 3/p + 2/q ≤ 3, 1 ≤  q <  ∞, or the $${L^{p,q}_{x,t}}$$ -norm of the gradient of the vorticity with 3/p + 2/q ≤ 4, 1 ≤  q, 1 ≤  p, is sufficiently small near z.

Subfields: Applied Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/1e96ee08a3b4091cea5b29f45428a0645ceebe2e

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In Applied Mathematics

1. Zhifei Zhang
2. Wendong Wang
3. Xixia Ma
4. Dapeng Du
5. Hongjie Dong
6. Vlad Vicol
7. Doyoon Kim
8. T. Buckmaster

In Control and Systems Engineering

1. Zhifei Zhang
2. Hongjie Dong
3. T. Buckmaster
4. Vlad Vicol

Citations in the corpus

• On the interior regularity criteria and the number of singular points to the Navier-Stokes equations (2014, background): “4 ([11]).”
• Partial regularity of Solutions of Navier-Stokes equations (2016, background): “Gustafson, Kang, and Tsai [4] generalize several previously known criteria.”
• The Navier-Stokes Equations in the Critical Lebesgue Space (2009, background): “For other results in this direction, we refer the reader to [31], [11], [3] and references therein.”