1998/07/29 by Yuxi Zheng, Tong Zhang, Zheng, Yuxi +1
Engineering · Mathematics · #35L65(primary) #35L67 #65M06 #65M99(secondary) #76N10 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #math.AP #msc:35L67 #msc:65M06 #msc:76N10
paper · pdf · doi:10.48550/arxiv.math/9807167
41pp, 14 figures, but 2 figures are separated from the main flow of text, they are named p4f1.1.ps and p4f1.2.ps
openalex publication_date 1998/07/29 · arxiv created 1998/07/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish rigorously the existence of a three-parameter family of self-similar,globally bounded, and continuous weak solutions in two space dimensions to the compressible Euler equations with axisymmetry for gamma-law polytropic gases with gamma between 1 and 2, including 1. The initial data of these solutions have constant densities and outward-swirling velocities. We use the axisymmetry and self-similarity assumptions to reduce the equations to a system of three ordinary differential equations, from which we obtain detailed structures of solutions besides their existence. These solutions exhibit familiar structures seen in hurricanes and tornadoes. They all have finite local energy and vorticity with well-defined initial and boundary values.