Shock-free Solutions of the Compressible Euler Equations
Geng Chen, Robin Young
TL;DR
This paper investigates the structure and behavior of large-data shock-free solutions to the compressible Euler equations, identifying conditions for character changes and vacuum formation, and providing new examples illustrating diverse dynamics.
Contribution
It introduces new conditions for character transitions and vacuum formation in shock-free solutions, along with novel examples demonstrating varied behaviors.
Findings
Conditions for character change are identified.
Vacuum formation criteria are established.
New examples of shock-free solutions are presented.
Abstract
We study the structure of shock-free solutions of the compressible Euler equations with large data. We describe conditions under which the Rarefactive/Compressive character of solutions changes, and conditions under which the vacuum is formed asymptotically. We present several new examples of shock-free solutions, which demonstrate a large variety of behaviors.
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Taxonomy
TopicsNavier-Stokes equation solutions · Advanced Mathematical Physics Problems · Computational Fluid Dynamics and Aerodynamics