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arXiv · 2210.10030

Quantitative control of solutions to the axisymmetric Navier-Stokes equations in terms of the weak $L^3$ norm

W. S. Ożański·S. Palasek
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Abstract

We are concerned with strong axisymmetric solutions to the $3$D incompressible Navier-Stokes equations. We show that if the weak $L^3$ norm of a strong solution $u$ on the time interval $[0,T]$ is bounded by $A \gg 1$ then for each $k\geq 0 $ there exists $C_k>1$ such that $\| D^k u (t) \|_{L^\infty (\mathbb{R}^3) } \leq t^{-(1+k)/2}\exp \exp A^{C_k}$ for all $t\in (0,T]$.

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W. S. Ożański, S. Palasek. 2022-10-18. Quantitative control of solutions to the axisymmetric Navier-Stokes equations in terms of the weak $L^3$ norm. https://arxiv.org/abs/2210.10030

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