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];L²(𝕋²)) the approximating velocity converges strongly in C([0,T];H¹(𝕋²)). Moreover, for the unique Yudovich solution of the 2D Euler equations we provide a rate of convergence for the velocity in C([0,T];L²(𝕋²)). 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];L²(𝕋²))
Convergence of the Euler-Voigt equations to the Euler equations in two dimensions
Luigi C. Berselli;Gianluca Crippa;Stefano Spirito
2025-01-01
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];L²(𝕋²)) the approximating velocity converges strongly in C([0,T];H¹(𝕋²)). Moreover, for the unique Yudovich solution of the 2D Euler equations we provide a rate of convergence for the velocity in C([0,T];L²(𝕋²)). 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];L²(𝕋²))I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
