Radially symmetric shadow wave solutions to the system of pressureless\n gas dynamics in arbitrary dimensions

2016/06/07 by Marko Nedeljkov, Nedeljkov, Marko, Lukas Neumann +5
Mathematics · Physics and Astronomy · #35L65 (Primary) #35L67 (secondary) #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1606.02100

openalex publication_date 2016/06/07 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Radially symmetric shadow wave solutions to the system of multidimensional\npressureless gas dynamics are introduced, which allow one to capture\nconcentration of mass. The transformation to a one-dimensional system with\nsource terms is performed and physically meaningful boundary conditions at the\norigin are determined. Entropy conditions are derived and applied to single out\nphysical (nonnegative mass) and dissipative (entropic) solutions. A complete\nsolution to the pseudo-Riemann problem with initial data exhibiting a single\nshock on a sphere is obtained.\n

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