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Abstract: We present in this note a unified approach on how to design simple, efficient and energy stable time discretization schemes for the Allen-Cahn or Cahn-Hilliard Navier-Stokes system which ...

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 ...