On the zero viscosity limit in incompressible fluids
نویسنده
چکیده
We discuss the convergence in the limit of vanishing viscosity of solutions of the Navier-Stokes equations for incompressible fluid flow to solutions of the Euler equations in the presence of boundaries. We present explicit examples in 2 and 3 dimensions for which convergence holds in the energy norm, even when the flow is forced through moving boundaries. We obtain convergence rates in viscosity and discuss concentration of vorticity at the boundary in the limit. PACS numbers: 47.27.N-,47.27.nb,47.15.-x,47.27.nd
منابع مشابه
The Inviscid Limit for Two-dimensional Incompressible Fluids with Unbounded Vorticity
In [C2], Chemin shows that solutions of the Navier-Stokes equations in R for an incompressible fluid whose initial vorticity lies in L ∩ L∞ converge in the zero-viscosity limit in the L–norm to a solution of the Euler equations, convergence being uniform over any finite time interval. In [Y2], Yudovich assumes an initial vorticity lying in L for all p ≥ p0, and establishes the uniqueness of sol...
متن کاملBKM’s Criterion and Global Weak Solutions for Magnetohydrodynamics with Zero Viscosity
In this paper we derive a criterion for the breakdown of classical solutions to the incompressible magnetohydrodynamic equations with zero viscosity and positive resistivity in R3. This result is analogous to the celebrated Beale-KatoMajda’s breakdown criterion for the inviscid Eluer equations of incompressible fluids. In R2 we establish global weak solutions to the magnetohydrodynamic equation...
متن کاملViscous potential flow
Potential flows u = ∇φ are solutions of the Navier–Stokes equations for viscous incompressible fluids for which the vorticity is identically zero. The viscous term μ∇u = μ∇∇φ vanishes, but the viscous contribution to the stress in an incompressible fluid (Stokes 1850) does not vanish in general. Here, we show how the viscosity of a viscous fluid in potential flow away from the boundary layers e...
متن کاملViscous effects on the Rayleigh-Taylor instability with background temperature gradient
The growth rate of the compressible Rayleigh-Taylor instability is studied in the presence of a background temperature gradient, Θ, using a normal mode analysis. The effect of Θ variation is examined for three interface types corresponding to combinations of the viscous properties of the fluids (inviscid-inviscid, viscous-viscous and viscous-inviscid) at different Atwood numbers, At, and, when ...
متن کاملOn the Limit as the Density Ratio Tends to Zero for Two Perfect Incompressible Fluids Separated by a Surface of Discontinuity
We study the asymptotic limit as the density ratio ρ−/ρ+ → 0, where ρ+ and ρ− are the densities of two perfect incompressible 2-D/3-D fluids, separated by a surface of discontinuity along which the pressure jump is proportional to the mean curvature of the moving surface. Mathematically, the fluid motion is governed by the two-phase incompressible Euler equations with vortex sheet data. By resc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008