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The regularity of semi‐hyperbolic patches near sonic curves for the two‐dimensional compressible magnetohydrodynamic equations
Author(s) -
Chen Jianjun,
Lai Geng
Publication year - 2020
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900016
Subject(s) - transonic , magnetohydrodynamic drive , compressibility , magnetohydrodynamics , compressible flow , flow (mathematics) , mathematical analysis , mathematics , physics , shock wave , hyperbolic partial differential equation , mechanics , partial differential equation , magnetic field , quantum mechanics , aerodynamics
This paper is concerned with the regularity of semi‐hyperbolic patches near sonic curves for the two‐dimensional (2D) compressible magnetohydrodynamic (MHD) equations. A semi‐hyperbolic patch is a flow in a region in which one family out of two families of wave characteristics start on sonic curve and end on transonic shock. This type of flow patterns appear frequently in solutions of 2D Riemann problems and transonic flow problems. In a recent study by Chen and Lai (Commun. Pure Appl. Anal. 18, 943–958 (2019)), we constructed a semi‐ hyperbolic patch for the 2D compressible MHD equations. In this paper, we derive a group of characteristic decompositions for the 2D MHD equations and show that the solution constructed in Chen and Lai (Commun. Pure Appl. Anal. 18, 943–958 (2019)) is smooth up to the sonic curve and the sonic curve is C 1 continuous.