2011/01/30 by S. Albeverio, Sergio Albeverio, Olga Rozanova +5
Engineering · Mathematics · Physics and Astronomy · #35L65 #35L67 #76L05 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35L65 #msc:35L67 #msc:76L05
paper · pdf · doi:10.48550/arxiv.1101.5815
18 pages
arxiv created 2011/01/30 · openalex publication_date 2011/01/30 · arxiv updated 2011/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce integral identities to define delta-shock wave type solutions for the multidimensional zero-pressure gas dynamics Using these integral identities, the Rankine-Hugoniot conditions for delta-shocks are obtained. We derive the balance laws describing mass, momentum, and energy transport from the area outside the delta-shock wave front onto this front. These processes are going on in such a way that the total mass, momentum, and energy are conserved and at the same time mass and energy of the moving delta-shock wave front are increasing quantities. In addition, the total kinetic energy transfers into the total internal energy. The process of propagation of delta-shock waves is also described. These results can be used in modeling of mediums which can be treated as a pressureless continuum (dusty gases, two-phase flows with solid particles or droplets, granular gases).