论文标题
在无粘性极限的2D Euler方程的涡度的强收敛
Strong convergence of the vorticity for the 2D Euler Equations in the inviscid limit
论文作者
论文摘要
在本文中，我们证明了$ 2D $ NAVIER-Stokes方程的家庭$ω^ν$的统一$ l^p $融合，用于欧拉方程的重新归一化/拉格朗日解决方案$ω$。我们还证明，在具有有限涡度的解决方案类别中，可以获得$ω^ν$在$ l^p $中的$ω^ν$到$ω$的收敛速率。最后，我们表明具有$ l^p $涡度的Euler方程的解决方案，以消失的粘度极限获得，保留了动能。这些证明是通过使用（随机）拉格朗日方法和Eulerian方法给出的。
In this paper we prove the uniform-in-time $L^p$ convergence in the inviscid limit of a family $ω^ν$ of solutions of the $2D$ Navier-Stokes equations towards a renormalized/Lagrangian solution $ω$ of the Euler equations. We also prove that, in the class of solutions with bounded vorticity, it is possible to obtain a rate for the convergence of $ω^ν$ to $ω$ in $L^p$. Finally, we show that solutions of the Euler equations with $L^p$ vorticity, obtained in the vanishing viscosity limit, conserve the kinetic energy. The proofs are given by using both a (stochastic) Lagrangian approach and an Eulerian approach.
