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廖家江 博士后：Zero-viscosity limit of the incompressible Navier-Stokes equations with sharp vorticity grad

本站小编 Free考研考试/2021-12-26


Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
Speaker: 廖家江 博士后，北京应用物理与计算数学研究所
Inviter:
Title:
 Zero-viscosity limit of the incompressible Navier-Stokes equations with sharp vorticity gradient
Time & Venue:
 2021.05.23 14:00-15:00 思源楼S803室
Abstract:
 It is well-known that the 3D incompressible Euler equations admit some local-in-time solutions for which the vorticity is piecewise smooth and discontinuous across a smooth time-dependent hypersurface which evolves with the ?ow. In this paper we prove that such a solution can be obtained as zero-viscosity limit of strong solutions to the Navier-Stokes equations whose vorticity has sharp variations near the hypersurface associated with the inviscid limit. Indeed we exhibit some sequences of exact solutions to the Navier-Stokes equations with vanishing viscosity which are given by multi-scale asymptotic expansions involving some characteristic boundary layers given by some linear PDEs. The convergence and the validity of the expan-sion are guaranteed on the time interval associated with the solution to the Euler equations.

相关话题/研究所 数学 计算 物理 北京

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