Title: Convergence of the Euler-Voigt equations to the Euler equations in two dimensions Show Chinese title

Title: 二维空间中欧拉-沃特方程到欧拉方程的收敛性

Abstract: In this paper, we consider the two-dimensional torus and we study the convergence of solutions of the Euler-Voigt equations to solutions of the Euler equations, under several regularity settings. More precisely, we first prove that for weak solutions of the Euler equations with vorticity in $C([0,T];L^2(\mathbb{T}^2))$ the approximating velocity converges strongly in $C([0,T];H^1(\mathbb{T}^2))$. Moreover, for the unique Yudovich solution of the $2D$ Euler equations we provide a rate of convergence for the velocity in $C([0,T];L^2(\mathbb{T}^2))$. Finally, for classical solutions in higher-order Sobolev spaces we prove the convergence with explicit rates of both the approximating velocity and the approximating vorticity in $C([0,T];L^2(\mathbb{T}^2))$. Show Chinese abstract

Abstract: 在本文中，我们考虑二维环面，并在几种正则性条件下研究欧拉-沃特方程解收敛到欧拉方程解的情况。 更准确地说，我们首先证明对于具有旋度在$C([0,T];L^2(\mathbb{T}^2))$中的欧拉方程的弱解，近似速度在$C([0,T];H^1(\mathbb{T}^2))$中强收敛。 此外，对于$2D$欧拉方程的唯一尤多维奇解，我们在$C([0,T];L^2(\mathbb{T}^2))$中提供了速度的收敛速率。 最后，对于高阶 Sobolev 空间中的经典解，我们证明了近似速度和近似旋度在$C([0,T];L^2(\mathbb{T}^2))$中的收敛具有显式速率。