The viscosity vanishing limit and global well-posedness of the three-dimensional incompressible Navier-Stokes equations with smooth large initial data in spherical coordinates

被引：3

作者：

Wang, Shu ^{[1
,2
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Peoples R China

[2] Beijing Univ Technol, Coll Appl Sci, Beijing 100124, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2020年 / 103卷

关键词：

Global smooth solution; Viscosity vanishing limit; Three-dimensional incompressible; Navier-Stokes equations; Euler equations; Spherical coordinates; WEAK SOLUTIONS; REGULARITY; FLUID;

D O I：

10.1016/j.aml.2019.106195

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper investigates the viscosity vanishing limit and the existence and uniqueness of the global strong solution on the three-dimensional incompressible Navier-Stokes equations without swirl in spherical coordinates. We establish the global existence and uniqueness of the smooth solution to the Cauchy problem for the three-dimensional incompressible Navier-Stokes equations for the any smooth large initial data without swirl in the sense of spherical coordinates. Also, by performing the viscosity vanishing limit for the global strong solution in time to the three-dimensional incompressible Navier-Stokes equations, we prove that there exists the unique and global strong solution to the Cauchy problem for the three-dimensional incompressible Euler equation without swirl in spherical coordinates with large initial data. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页数：6

共 16 条

[1]

Bachelor G.K., 1967, INTRO FLUID DYNAMICS

[2] PARTIAL REGULARITY OF SUITABLE WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS [J].