Abstract
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).
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Chen, Q., Miao, C. & Zhang, Z. On the Well-posedness of the Ideal MHD Equations in the Triebel–Lizorkin Spaces. Arch Rational Mech Anal 195, 561–578 (2010). https://doi.org/10.1007/s00205-008-0213-6
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DOI: https://doi.org/10.1007/s00205-008-0213-6