An Eulerian-Lagrangian Approach for Incompressible Fluids: Local Theory
Analysis of PDEs
2007-05-23 v1 Dynamical Systems
Abstract
We present a local existence result for the three dimensional incompressible Euler equations. The solution is constructed using a formulation of the equations as an active vector system in Eulerian coordinates. The formulation employs the inverse of the Lagrangian path map (the "back-to-labels" map) and its Eulerian gradient. We express sufficient conditions for regularity in terms of this gradient.
Cite
@article{arxiv.math/0004059,
title = {An Eulerian-Lagrangian Approach for Incompressible Fluids: Local Theory},
author = {P. Constantin},
journal= {arXiv preprint arXiv:math/0004059},
year = {2007}
}