The Initial Boundary Value Problem for Navier-Stokes Equations

作     者：Cheng He, Institute of Applied Mathmatics, Academia Sinica, Beijing 100080, P. R. ChinaE-mail: cheng@*** 

作者机构：Institute of Applied Mathmatics Academia Sinica Beijing P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：1999年第15卷第2期

页      面：153-164页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work is supported by foundation of Institute of Mathematics  Academia Sinica 

主　　题：Navier-Stokes equations Stokes equations Homogeneous boundary conditions Nonhomogeneous boundary conditions 

摘      要：By making full use of the estimates of solutions to nonstationary Stokes equations and the method discussing global stability, we establish the global existence theorem of strong solutions for Navier-Stokes equations in arbitrary three dimensional domain with uniformly C3 boundary, under the assumption that ‖a‖L^2(Ω)+‖f‖L^1(o,∞;L^2(Ω)) or‖▽a‖L^2(Ω)+‖f‖L^2(o,∞;L^2(Ω)) small or viscosity, large. Here a is a given initial velocity and f is the external force. This improves on the previous results. Moreover, the solvability of the case with nonhomogeneous boundary conditions is also discussed.