Global existence of a classical solution for the isentropic nozzle flow

2024/02/07 by Shih‐Wei Chou, Bo-Chih Huang, Chou, Shih-Wei +5
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2402.05268

openalex publication_date 2024/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Our goal in this paper is to prove the global existence of a classical solution for the isentropic nozzle flow. Regarding this problem, there exist some global existence theorems of weak solutions. However, that of classical solutions does not have much attention until now. When we consider the present problem, the main difficulty is to obtain the uniform bound of solutions and their derivatives. To solve this, we introduce an invariant region depending on the space variable and a functional satisfying the Riccati equation along the characteristic lines.

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