Remarks on High Reynolds Numbers Hydrodynamics and the Inviscid Limit
Remarks on High Reynolds Numbers Hydrodynamics and the Inviscid Limit
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DOI：
10.1007/s00332-017-9424-z
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发表时间：
2017-08
影响因子：
3
通讯作者：
P. Constantin;V. Vicol
中科院分区：
文献类型：
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作者：
P. Constantin;V. Vicol
证明了Navier-Stokes方程的一组强解在有界域上的任何弱时空消失黏度极限都满足欧拉方程，如果解的局部熵是一致有界的。我们还证明了三维Navier-Stokes方程在有界区域上解的弱无粘极限在局部满足二阶结构函数的标度性质时是欧拉方程的弱解。所施加的条件远离边界，欧拉方程的野解并非先验地排除在极限之外。
We prove that any weak space-timevanishing viscosity limit of a sequence of strong solutions of Navier–Stokes equations in a bounded domain ofsatisfies the Euler equation if the solutions’ local enstrophies are uniformly bounded. We also prove thatweakinviscid limits of solutions of 3D Navier–Stokes equations in bounded domains are weak solutions of the Euler equation if they locally satisfy a scaling property of their second-order structure function. The conditions imposed are far away from boundaries, and wild solutions of Euler equations are not a priori excluded in the limit.