Archive for Rational Mechanics and Analysis

, Volume 195, Issue 2, pp 561-578

First online:

On the Well-posedness of the Ideal MHD Equations in the Triebel–Lizorkin Spaces

  • Qionglei ChenAffiliated withInstitute of Applied Physics and Computational Mathematics
  • , Changxing MiaoAffiliated withInstitute of Applied Physics and Computational Mathematics Email author 
  • , Zhifei ZhangAffiliated withSchool of Mathematical Science, Peking University

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In this paper, we prove the local well-posedness for the ideal MHD equations in the Triebel–Lizorkin spaces and obtain a blow-up criterion of smooth solutions. Specifically, we fill a gap in a step of the proof of the local well-posedness part for the incompressible Euler equation in Chae (Comm Pure Appl Math 55:654–678 2002).