A Lagrangian Scheme à la Brenier for the Incompressible Euler Equations

In the present paper, we study the fast rotation limit for the density-dependent incompressible Euler equations in two space dimensions with the presence of the Coriolis force.. In

An essential feature of the studied scheme is that the (discrete) kinetic energy remains controlled. We show the compactness of approximate sequences of solutions thanks to a

The method consists in embedding the incompressible Euler equation with a potential term coming from classical mechanics into incompressible Euler of a manifold and seeing the

us naturally to the notion of boundary-coupled weak solution. We have defined boundary-coupled weak solution using the vorticity formulation of the Euler equations. However, in order

The functional framework that we shall adopt – Besov spaces embedded in the set C 0,1 of bounded globally Lipschitz functions – is motivated by the fact that the density and

Figure 12: Relative difference between the computed solution and the exact drift-fluid limit of the resolved AP scheme at time t = 0.1 for unprepared initial and boundary conditions ε

Our approach combines Arnold’s interpretation of the solution of Euler’s equation for incompressible and inviscid flu- ids as geodesics in the space of

Galerkin-truncated dynamics of these two equations behave very differently in comparison to their non truncated counterparts: for the 2D Euler equations we have shown weak