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L ∞ continuation principle to the non‐baratropic non‐resistive magnetohydrodynamic equations without heat conductivity
Author(s) -
Huang Xiangdi,
Wang Yun
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3860
Subject(s) - magnetohydrodynamic drive , continuation , mathematics , bounded function , magnetohydrodynamics , thermal conductivity , magnetic field , mathematical analysis , conductivity , resistive touchscreen , electrical resistivity and conductivity , compressibility , carnot cycle , physics , thermodynamics , quantum mechanics , engineering , computer science , electrical engineering , programming language
The aim of this paper is to establish a continuation principle for strong solutions to the full compressible magnetohydrodynamic system without resistivity and heat conductivity. We prove that if the solution loses its regularity in finite time, the dominated part is due to the hyperbolic effect. More precisely, it is essentially shown that the strong solution exists globally if the density, temperature, and magnetic field are bounded from above, where vacuum is allowed to exist. This verifies a problem proposed by D.Serre. Copyright © 2016 John Wiley & Sons, Ltd.