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An Eulerian-Lagrangian Approach for Incompressible Fluids: Local Theory

P. Constantin
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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.

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P. Constantin. 2000-04-10. An Eulerian-Lagrangian Approach for Incompressible Fluids: Local Theory. https://arxiv.org/abs/math/0004059

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