2018/04/25 by Eduard Feireisl, Christian Klingenberg, Simon Markfelder · 25 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Backward Euler method #Classical mechanics #Compressibility #Compressible flow #Computer science #Dispersion (optics) #Dissipative system #Euler equations #Euler system #Euler's formula #Fluid Dynamics and Turbulent Flows #Inviscid flow #Limit (mathematics) #Mach number #Mathematical analysis #Mathematics #Measure (data warehouse) #Mechanics #Navier-Stokes equation solutions #Physics #Semi-implicit Euler method #Zero (linguistics) #math.AP
paper · pdf · doi:10.1137/17m1131799
published in SIAM Journal on Mathematical Analysis 51(2), 1496-1513 (Society for Industrial and Applied Mathematics)
arxiv created 2018/04/25 · openalex publication_date 2019/01/01 · arxiv updated 2019/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper, we propose a new approach to singular limits of inviscid fluid flows based on the concept of dissipative measure-valued solutions. We show that dissipative measure-valued solutions of the compressible Euler equations converge to the smooth solution of the incompressible Euler system when the Mach number tends to zero. This holds both for well-prepared and ill-prepared initial data, where in the latter case the presence of acoustic waves causes difficulties. However this effect is eliminated on certain unbounded domains and, in particular, on the whole space, thanks to dispersion.