The regularity of semi-hyperbolic patches of solutions to the two-dimensional compressible Euler equations in magnetohydrodynamics

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-01-13 DOI:10.1016/j.jmaa.2025.129242

Jianjun Chen, Yuqi Zhang, Shuangrong Li

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引用次数: 0

Abstract

The semi-hyperbolic patches appear frequently in solutions of multi-dimensional Riemann problem and transonic flow problems. We have obtained a semi-hyperbolic patch solution for the two-dimensional compressible magnetohydrodynamic equations (Chen and Geng, 2019 [4]). Subsequently, we prove the semi-hyperbolic patch solution is smooth up to the sonic curve and sonic curve is

C^{1}

continuous (Chen and Geng, 2020 [5]). This paper will further consider the regularity of semi-hyperbolic patch problem to the two-dimensional compressible Euler equations in magnetohydrodynamics. By constructing an appropriate variable and using characteristic decomposition and bootstrap method, we show that the semi-hyperbolic patch solution is

C^{1, \frac{1}{6}}

up to the sonic curve and sonic curve is also

C^{1, \frac{1}{6}}

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.