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| Remarks on Vanishing Viscosity Limits for the 3D Navier-Stokes Equations with a Slip Boundary Condition |
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Citation： |
Yuelong XIAO,Zhouping XIN.Remarks on Vanishing Viscosity Limits for the 3D Navier-Stokes Equations with a Slip Boundary Condition[J].Chinese Annals of Mathematics B,2011,32(3):321~332 |
| Page view： 2038
Net amount： 1818 |
Authors： |
Yuelong XIAO; Zhouping XIN; |
Foundation： |
the National Natural Science Foundation of China (No. 10971174), the Scientific
Research Fund of Hunan Provincial Education Department (No. 08A070), the Zheng Ge Ru Foundation,
the Hong Kong RGC Earmarked Research Grants (Nos. CUHK-4040/06P, CUHK-4042/08P) and a Focus
Area Grant at The Chinese University of Hong Kong. |
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| Abstract： |
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];H1(Ω)) provided that the initial vorticity vanishes on the boundary
of the domain. |
Keywords： |
Poincar′e inequality, Sobolev spaces with variable exponent |
Classification： |
26D10, 26D15, 46E30, 46E35 |
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