A certain necessary condition of potential blow up for Navier-Stokes equations

By G.Seregin. 2011

108 citations recorded by the source corpus.

We show that a necessary condition for T to be a potential blow up time is lim t↑T ‖v(·, t)‖L3 = ∞. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.

Subfields: Applied Mathematics, Computational Mechanics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/c9a2bbb775580f3f62f037b7821e506de2da9ca8

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In Applied Mathematics

1. Terence Tao
2. Sanghyuk Lee
3. D. Tataru
4. Zihua Guo
5. Carlos E. Kenig
6. Jonathan Bennett
7. Shuanglin Shao
8. Jean Bourgain

In Computational Mechanics

1. Terence Tao
2. E.J. Candes
3. Richard Baraniuk
4. Martin J. Wainwright
5. Justin K. Romberg
6. David L. Donoho
7. Cun-Hui Zhang
8. Yonina C. Eldar

In Control and Systems Engineering

1. Terence Tao
2. E.J. Candes
3. Suhas N. Diggavi
4. David L. Donoho
5. Martin J. Wainwright
6. Tong Zhang
7. Cun-Hui Zhang
8. René Vidal

Citations in the corpus

• Blow-up of Critical Besov Norms at a Potential Navier–Stokes Singularity (2014, unknown): “1In the L(3)(R(3)) setting of [6], it was recently shown in [23] that moreover (for Leray-Hopf weak solutions) one can replace lim supt→T∗ ‖u(t)‖L3 = ∞ by limt→T∗ ‖u(t)‖L3 = ∞ for a singular time T ∗ < ∞.”
• Quantitative bounds for critically bounded solutions to the Navier-Stokes equations (2019, background): “1 with a limit, as is done in [17] (see also [1]); again, it may be possible to also find quantitative analogues of these results, but we do not pursue this matter here.”