Large time behavior of strong solutions to the 1D non-resistive full compressible MHD system with large initial data

  • Xin Si
  • Xiaokui Zhao


The Cauchy and initial-boundary value problems for one-dimensional compressible magnetohydrodynamics (MHD) system with non-resistive are studied in this article. Global-in-time, strong solutions to this system are shown to exist uniquely and be asymptotically stable as the time tends to infinity for large initial data. The main difficulties lie in the uniform-in-time estimate of first-order derivative of magnetic and the estimates of positive lower and upper uniform-in-time bounds of the density and temperature. This is a development of Zhang and Zhao (J Math Phys 58:031504, 2017).


Magnetohydrodynamics (MHD) Non-resistive Large time behavior Large initial data 

Mathematics Subject Classification

35Q35 35B45 35Q60 76N10 76X05 



The authors are grateful to the anonymous referees for their valuable comments and helpful suggestions that have contributed to the final version of the paper.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Applied MathematicsXiamen University of TechnologyXiamenPeople’s Republic of China
  2. 2.School of Mathematical SciencesXiamen UniversityXiamenPeople’s Republic of China

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