Global solutions of shock reflection problem for the pressure gradient system

Hanchun Yang; Meimei Zhang; Qin Wang

doi:10.3934/cpaa.2020150

Article Contents

2020, Volume 19, Issue 6: 3387-3428. Doi: 10.3934/cpaa.2020150

This issue Previous Article The probabilistic Cauchy problem for the fourth order Schrödinger equation with special derivative nonlinearities Next Article Existence results for quasilinear Schrödinger equations with a general nonlinearity

Global solutions of shock reflection problem for the pressure gradient system

Department of Mathematics and Statistics, Yunnan University, Kunming, 650091, China

^* Corresponding author
^* Corresponding author

Received: November 30, 2019

Revised: November 30, 2019

Published: March 2020

The first author is supported by NSF of Yunnan University (No. 2019FY003007). The third author is supported by National Natural Science Foundation of China (No. 11761077) and Key Project of Yunnan Provincial Science and Technology Department and Yunnan University (No. 2018FY001(-014))

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Abstract

We are concerned with the shock reflection in gas dynamics for the pressure gradient system. Experimental and computational analysis has shown that two patterns of regular reflection may occur: supersonic and subsonic reflection. In this paper we establish the global existence of solutions for both configurations. The ideas and techniques developed here will be useful for the two-dimensional Riemann problems for hyperbolic conservation laws.

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Mathematics Subject Classification: Primary: 35L50, 35L67, 76H05; Secondary: 35J67.

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Figure 1. Supersonic regular shock reflection configuration(left); subsonic regular shock reflection configuration (right)}

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Figure 2. Hypothetical curves

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