A review on two types of sonic interfaces

2024/05/09 by Myoungjean Bae, Bae, Myoungjean
Computer Science · Neuroscience · #35C06 #35M10 #35M30 #35Q31 #76H05 #76N10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Music Technology and Sound Studies #Tactile and Sensory Interactions

paper · pdf · doi:10.48550/arxiv.2405.05717

openalex publication_date 2024/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

In this paper, two examples of sonic interfaces are presented. The first example shows the case of sonic interfaces as weak discontinuities in self-similar shock configurations of unsteady Euler system. The second example shows the case of sonic interfaces as regular interfaces in accelerating transonic flows governed by the steady Euler-Poisson system with self-generated electric forces. And, we discuss analytic differences of the two examples, and introduce an open problem on decelerating transonic solution to the steady Euler-Poisson system.

Related

• The steady Euler-Poisson system and accelerating flows with transonic C¹-transitions
• Smooth Transonic Flows in De Laval Nozzles
• Convexity of Self-Similar Transonic Shocks and Free Boundaries for the Euler Equations for Potential Flow
• Supersonic sonic patch solution for the two-dimensional Euler equations with a van der Waals equation of state
• Classical solutions to a mixed-type PDE with a Keldysh-type degeneracy and accelerating transonic solutions to the Euler-Poisson system