论文标题
对洛伦兹空间中三维纳维尔 - 斯托克斯方程的关键解决方案的定量界限
Quantitative bounds for critically bounded solutions to the three-dimensional Navier-Stokes equations in Lorentz spaces
论文作者
论文摘要
在本文中，我们证明了针对三维Navier-Stokes方程的经典解决方案的定量规律定理和爆炸标准。通过调整Tao在[20]中制定的策略，我们在关键Lorentz空间的设置中获得了明确的爆炸率$ l^{3，q_ {0}}（\ Mathbb r^3）$，$ 3 \ leq q_0 <\ infty $。我们的结果改善了[20]中关键Lebesgue空间的先前规律性$ l^3（\ Mathbb r^3）$，并在[16]中量化了PHUC的定性结果。
In this paper, we prove a quantitative regularity theorem and a blow-up criterion of classical solutions for the three-dimensional Navier-Stokes equations. By adapting the strategy developed by Tao in [20], we obtain an explicit blow-up rate in the setting of critical Lorentz spaces $L^{3, q_{0}}(\mathbb R^3)$ with $3 \leq q_0 < \infty $. Our results improve the previous regularity in critical Lebesgue spaces $L^3(\mathbb R^3)$ in [20] and quantify the qualitative result by Phuc in [16].
