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arXiv · 1808.10297

Energy conservation for inhomogeneous incompressible and compressible Euler equations

Quoc-Hung Nguyen·Phuoc-Tai Nguyen·Bao Quoc Tang
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Abstract

Energy conservations are studied for inhomogeneous incompressible and compressible Euler equations with general pressure law in a torus or a bounded domain. We provide sufficient conditions for a weak solution to conserve the energy. By exploiting a suitable test function, the spatial regularity for the density is only required to be of order $2/3$ in the incompressible case, and of order $1/3$ in the compressible case. When the density is constant, we recover the existing results for classical incompressible Euler equation.

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Quoc-Hung Nguyen, Phuoc-Tai Nguyen, Bao Quoc Tang. 2018-08-30. Energy conservation for inhomogeneous incompressible and compressible Euler equations. https://arxiv.org/abs/1808.10297

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