Energy conservation for inhomogeneous incompressible and compressible\n Euler equations

2018/08/30 by Quoc‐Hung Nguyen, Nguyen, Quoc-Hung, Phuoc‐Tai Nguyen +3 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1808.10297

openalex publication_date 2018/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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