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arXiv · 2409.13414

An Eulerian-Lagrangian Formulation of the Compressible Euler Equations with Vacuum

Wladimir Neves·Christian Olivera
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Abstract

In this paper, we present a novel Eulerian-Lagrangian formulation for the compressible isentropic Euler equations with vaccum. Using the developed Lagrangian flow map formulation, we show a short-time solution for a general pressure law. A particularly appealing feature of the approach used, it is well defined in the presence of vacuum, namely for compactly supported initial data which constitute an important problem in gas dynamics. Moreover, it does so without relying on any special symmetrization. While analogous results are well understood for incompressible fluids, the compressible setting, particularly in the presence of vacuum, remained open.

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Wladimir Neves, Christian Olivera. 2024-09-20. An Eulerian-Lagrangian Formulation of the Compressible Euler Equations with Vacuum. https://arxiv.org/abs/2409.13414

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