Low-Mach-number Euler equations with solid-wall boundary condition and general initial data

2010/06/06 by Bin Cheng, Cheng, Bin
Engineering · Mathematics · #35Q31 (Primary) 35L50 #76N15 (Secondary) #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1006.1148

openalex publication_date 2010/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the divergence-free component of the compressible Euler equations with solid-wall boundary condition converges strongly towards the incompressible Euler equations at the same order as the Mach number. General initial data are considered and are not necessarily close to the divergence-free state. Thus, large amplitude of fast oscillations persist and interact through nonlinear coupling without any dissipative or dispersive mechanism. It is then shown, however, that the contribution from fast oscillations to the slow dynamics through nonlinear coupling is of the same order as the Mach number when averaged in time. The structural condition of a vorticity equation plays a key role in our argument.

Citations

• Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids

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