论文标题
根据初始数据的$ε$ - 型号标准和Navier-Stokes流的常规集估算值
An $ε$-regularity criterion and estimates of the regular set for Navier-Stokes flows in terms of initial data
论文作者
论文摘要
根据初始数据，我们证明了3D Navier-Stokes方程的$ε$ -Regulacularity标准。它表明，如果缩放的本地$ l^2 $初始数据的规范在原点周围足够小，则适当的弱解决方案是常规的，该解决方案是在抛物面启动的一组中。结果应用于对本地能源解决方案的常规估算，并具有加权$ l^2 $空间的初始数据。我们还将这一结果应用于在可能的爆炸时间和正向离散自相似解决方案的规律性附近研究能量浓度。
We prove an $ε$-regularity criterion for the 3D Navier-Stokes equations in terms of initial data. It shows that if a scaled local $L^2$ norm of initial data is sufficiently small around the origin, a suitable weak solution is regular in a set enclosed by a paraboloid started from the origin. The result is applied to the estimate of the regular set for local energy solutions with initial data in weighted $L^2$ spaces. We also apply this result to studying energy concentration near a possible blow-up time and regularity of forward discretely self-similar solutions.
