论文标题
Navier-Stokes方程的轻度关键破坏
Mild criticality breaking for the Navier-Stokes equations
论文作者
论文摘要
在这篇简短的论文中，我们证明了在略微超临界数量有限的假设下，对Navier-Stokes方程的解决方案的全球规律性。结果，我们证明，如果对Navier-Stokes方程的解决方案$ u $会爆炸，那么某些略微超临界规范就必须无限制。这部分回答了Terence Tao最近做出的猜想。证明依赖于临界水平的定量规律性估计，并在初始数据上转移亚临界信息到任意的时间。该方法的灵感来自最近的Aynur Bulut论文，在该论文中，对于能量超临界非线性schrödinger方程而言，类似的结果被证明。
In this short paper we prove the global regularity of solutions to the Navier-Stokes equations under the assumption that slightly supercritical quantities are bounded. As a consequence, we prove that if a solution $u$ to the Navier-Stokes equations blows-up, then certain slightly supercritical Orlicz norms must become unbounded. This partially answers a conjecture recently made by Terence Tao. The proof relies on quantitative regularity estimates at the critical level and transfer of subcritical information on the initial data to arbitrarily large times. This method is inspired by a recent paper of Aynur Bulut, where similar results are proved for energy supercritical nonlinear Schrödinger equations.
