In this article, we consider a non-local variant of the Kuramoto-Sivashinsky equation in three dimensions (2D interface). Besides showing global wellposedness also obtain some qualitative properties solutions. particular, prove that solutions become analytic spatial variable for positive time, existence compact attractor and an upper bound on number oscillations We observe such is particularly ...

Model order reduction through the POD-Galerkin method can lead to dramatic gains in terms of computational efficiency solving physical problems. However, applicability non linear high-dimensional dynamical systems such as Navier–Stokes equations has been shown be limited, producing inaccurate and sometimes unstable models. This paper proposes a deep learning based closure modeling approach for ...