Remarks on the Emergence of Weak Euler Solutions in the Vanishing Viscosity Limit
Remarks on the Emergence of Weak Euler Solutions in the Vanishing Viscosity Limit
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DOI：
10.1007/s00332-018-9500-z
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发表时间：
2019-04-01
影响因子：
3
通讯作者：
Nguyen, Huy Q.
中科院分区：
文献类型：
--
作者：
Drivas, Theodore D.;Nguyen, Huy Q.
证明了：若在惯性范围内局部二阶结构函数指数在粘性上一致保持正，则在Rd，d= 2，3的任意有界区域Ω子集上的Navier-Stokes方程的Leray-Hopf弱解的时空L2弱极限是Euler方程的弱解.这适用于无滑移和Navier摩擦条件与粘度依赖的滑移长度。结果允许出现的非唯一的，可能是耗散的，限制弱解的欧拉方程。
We prove that if the local second-order structure function exponents in the inertial range remain positive uniformly in viscosity, then any spacetime L2 weak limit of Leray-Hopf weak solutions of the Navier-Stokes equations on any bounded domain Omega subset of Rd, d=2,3 is a weak solution of the Euler equations. This holds for both no-slip and Navier friction conditions with viscosity-dependent slip length. The result allows for the emergence of non-unique, possibly dissipative, limiting weak solutions of the Euler equations.