关于3D不可压Navier-Stokes方程H¹正则性的注记  

A Note on the H1 Regularity of 3D Incompressible Navier-Stokes Equation

作　　者：杨成明 崔振琼 

机构地区：[1]上海师范大学,上海

出　　处：《应用数学进展》2021年第7期2529-2552,共24页Advances in Applied Mathematics

摘　　要：这篇论文主要研究了3D不可压Navier-Stokes方程解的H1正则性. 首先, 本论文给出井详细证明 了3D不可压Navier-Stokes方程解的局部适定性引理. 其次, 应用上述解的局部适定性引理, 第一, 可以严格证明解在小初始数据情形时的全局正则性. 第二, 对于最大可能的所有U0和最大可能的所 有F , 证明出3D不可压Navier-Stokes方程解的H1 正则性. 本论文强调不仅对最大可能U0和某一 固定F 这一情形, 解具有H1正则性, 而且对最大可能U0和最大可能的F 这一情形, 解同样具有H1正则性。In this paper, we mainly study the H1 regularity of the solution of 3D incompressible Navier-Stokes equations. Firstly, the local well-fit lemma for solutions of 3D incom- pressible Navier-Stokes equations is given and proved in detail. Secondly, by applying the local well-fit lemma of the solution mentioned above, firstly, the global regularity of the solution in the case of small initial data can be proved strictly. Second, the H1 regularity of the solution of 3D incompressible Navier-Stokes equations is proved for all possible U0 and all possible F . In this paper, it is emphasized that the solution is H1 regular not only for the maximum possible U0 and a fixed F , but also for the maximum possible U0 and the maximum possible F .

关 键 词：H¹正则性 局部适定性引理 3D不可压Navier-Stokes方程 

分 类 号：O17[理学—数学]