A note on helicity conservation for compressible Euler equations in a bounded domain with vacuum

2025/05/26 by Yulin Ye, Ye, Yulin
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2505.20080

openalex publication_date 2025/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the helicity conservation of weak solutions for the compressible Euler equations in a bounded domain with general pressure law and vacuum. We deduce a sufficient condition for a weak solution conserving the helicity based on the interior Besov-VMO type regularity, the continuous conditions for velocity and vorticity near the boundary, and some regularities for density near vacuum.

Citations

• The helicity distribution for the 3D incompressible Euler equations
• On the conservation of helicity by weak solutions of the 3D Euler and inviscid MHD equations
• Analytical validation of the helicity conservation for the compressible Euler equations
• Energy equality in the isentropic compressible Navier-Stokes equations allowing vacuum
• Onsager's conjecture in bounded domains for the conservation of entropy and other companion laws
• On the Helicity conservation for the incompressible Euler equations
• Energy and cross-helicity conservation for the three-dimensional ideal MHD equations in bounded domain
• Energy conservation for inhomogeneous incompressible and compressible\n Euler equations
• Renormalization of active scalar equations
• Onsager's energy conservation for inhomogeneous Euler equations
• A Proof of Onsager's Conjecture
• The Energy Balance Relation for Weak solutions of the Density-Dependent\n Navier-Stokes Equations
• Dissipative Euler Flows and Onsager's Conjecture
• On the energy of inviscid singular flows
• Statistical hydrodynamics

Related

• Analytical validation of the helicity conservation for the compressible Euler equations
• Energy conservation for inhomogeneous incompressible and compressible\n Euler equations
• On the Helicity conservation for the incompressible Euler equations
• On the removal of the barotropic condition in helicity studies of the compressible Euler and ideal compressible MHD equations
• The compressible Euler equations in a physical vacuum: a comprehensive Eulerian approach