Abstract. It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian dynamical system in a manifold, one can consider it as geometric equipment of this manifold. Then properties of other dynamical systems can be studied rela...

We consider solutions to the two-dimensional incompressible Euler system with only integrable vorticity, thus with possibly locally infinite energy. With such regularity, we use the recently developed theory of Lagrangian flows associated to vector fields with gradient given by a singular integral in order to define Lagrangian solutions, for which the vorticity is transported by the flow. We pr...

A framework for embedding a Lagrangian model within ocean climate models that employ horizontal Eulerian grids is presented. The embedded Lagrangian model can be used to explicitly represent processes that are at the subgrid scale to the Eulerian model. The framework is applied to open ocean deep convection and gravity driven downslope flows, both of which are subgridscale in the present genera...

This paper introduces a geometrically constrained variational problem for the area functional. We consider the area restricted to the lagrangian surfaces of a Kähler surface, or, more generally, a symplectic 4-manifold with suitable metric, and study its critical points and in particular its minimizers. We apply this study to the problem of finding canonical representatives of the lagrangian ho...

Different implementations on a massively parallel computer system of a semi-Lagrangian method within the numerical weather forecast model HIRLAM are presented. In principle semi-Lagrangian methods on massively parallel architectures result in irregular communications, i.e., communications between arbitrary processors. It is shown that the fastest implementationincreases the total execution time...

We introduce a new method for studying the Cauchy problem for systems of conservation laws in one space dimension. This method is based on the equivalence of the Cauchy problems in Eulerian and Lagrangian coordinates, as regards the existence and uniqueness of entropy solutions. The main idea is to solve the problem in Lagrangian coordinates and determine the transformation linking the two coor...

The Principle of Least Action is used with a simple Lagrangian density, involving second-order derivatives of the wave function, to obtain the Schrödinger equation. A Hamiltonian density obtained from this simple Lagrangian density shows that Hamilton’s equations also give the Schrödinger equation. This simple Lagrangian density is equivalent to a standard Lagrangian density with first-order de...

Abstract. The recently developed theory of Lagrangian flows for transport equations with low regularity coefficients enables to consider non BV vector fields. We apply this theory to prove existence and stability of global Lagrangian solutions to the repulsive Vlasov-Poisson system with only integrable initial distribution function with finite energy. These solutions have a well-defined Lagrang...

The recently developed theory of Lagrangian flows for transport equations with low regularity coefficients enables to consider non BV vector fields. We apply this theory to prove existence and stability of global Lagrangian solutions to the repulsive Vlasov-Poisson system with only integrable initial distribution function with finite energy. These solutions have a well-defined Lagrangian flow. ...