In this paper we prove the uniform-in-time $L^2$ convergence for the Fourier-Galerkin approximation to Yudovich solutions of the $2D$ Euler equations. Precisely, we show that both the approximating velocity and the approximating vorticity converge strongly in $C(L^2)$. Moreover, for the convergence of the velocity we provide a rate fo convergence. The proofs are based on a relative entropy approach and the Osgood's lemma.
Fourier-Galerkin approximation of the 2D Euler equations with bounded vorticity
Luigi C. Berselli
;Stefano Spirito
2024-01-01
Abstract
In this paper we prove the uniform-in-time $L^2$ convergence for the Fourier-Galerkin approximation to Yudovich solutions of the $2D$ Euler equations. Precisely, we show that both the approximating velocity and the approximating vorticity converge strongly in $C(L^2)$. Moreover, for the convergence of the velocity we provide a rate fo convergence. The proofs are based on a relative entropy approach and the Osgood's lemma.File in questo prodotto:
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