论文标题
适合不可压缩的Navier-Stokes方程的良好性，平稳性和爆炸
Well-posedness, Smoothness and Blow-up for Incompressible Navier-Stokes Equations
论文作者
论文摘要
For any divergence free initial datum $u_0$ with $\|u_0\|_\infty+\|\nabla u_0\|_{L^p}+\|\nabla^2 u_0\|_{L^p}<\infty$ for some $p>d\ (d\ge 2)$, the well-posedness and smoothness are proved for不可压缩的navier在$ \ mathbb {r}^d $或$ \ mathbb {t}^d：= \ mathbb {r}^d/\ mathbb {z}^d，$最多明确地给出了来自初始数据和三个常数的时间，来自热量凯尔和ries rie kern ries rie kersel rie kern theforme。对于$ l^p $结合的初始数据，也证明了温和的良好性。对于两种类型的解决方案的最大时间都证明了爆炸。
For any divergence free initial datum $u_0$ with $\|u_0\|_\infty+\|\nabla u_0\|_{L^p}+\|\nabla^2 u_0\|_{L^p}<\infty$ for some $p>d\ (d\ge 2)$, the well-posedness and smoothness are proved for incompressible Navier-Stokes equations on $\mathbb{R}^d$ or $\mathbb{T}^d:=\mathbb{R}^d/\mathbb{Z}^d,$ up to a time explicitly given by the initial datum and three constants coming from the upper bounds of the heat kernel and the Riesz transform. A mild well-posedness is also proved for $L^p$-bounded initial data. The blow-up is proved for both type solutions with finite maximal time.
