The authors study vanishing viscosity limits of solutions to the 3-dimensional incompressible Navier-Stokes system in general smooth domains with curved boundaries for a class of slip boundary conditions. In contrast ...The authors study vanishing viscosity limits of solutions to the 3-dimensional incompressible Navier-Stokes system in general smooth domains with curved boundaries for a class of slip boundary conditions. In contrast to the case of flat boundaries, where the uniform convergence in super-norm can be obtained, the asymptotic behavior of viscous solutions for small viscosity depends on the curvature of the boundary in general. It is shown, in particular, that the viscous solution converges to that of the ideal Euler equations in C（[0, T]; HI（Ω）） provided that the initial vorticity vanishes on the boundary of the domain.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10971174)the Scientific Research Fund of Hunan Provincial Education Department(No.08A070)+1 种基金the Zheng Ge Ru Foundation, the Hong Kong RGC Earmarked Research Grants(Nos.CUHK-4040/06P,CUHK-4042/08P)a Focus Area Grant at The Chinese University of Hong Kong
文摘The authors study vanishing viscosity limits of solutions to the 3-dimensional incompressible Navier-Stokes system in general smooth domains with curved boundaries for a class of slip boundary conditions. In contrast to the case of flat boundaries, where the uniform convergence in super-norm can be obtained, the asymptotic behavior of viscous solutions for small viscosity depends on the curvature of the boundary in general. It is shown, in particular, that the viscous solution converges to that of the ideal Euler equations in C（[0, T]; HI（Ω）） provided that the initial vorticity vanishes on the boundary of the domain.
