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<p>We study the two-dimensional MHD boundary layer equations. For a small perturbation around a tangential background magnetic field, we obtain the global-in-time existence and uniqueness of solutions in Sobolev spaces. The proof relies on the novel combination of the well-explored cancellation mechanism and the idea of linearly-good unknowns, and we use the former idea to deal with the top tangential derivatives and the latter one admitting fast decay rates to control lower-order derivatives.</p>

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Global well-posedness of the MHD boundary layer equations in the Sobolev space

  • 期刊论文

  • 发表日期：

    2025年11月5日

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  • Wei-Xi Li,
  • Zhan Xu,
  • Anita Yang

摘要

We study the two-dimensional MHD boundary layer equations. For a small perturbation around a tangential background magnetic field, we obtain the global-in-time existence and uniqueness of solutions in Sobolev spaces. The proof relies on the novel combination of the well-explored cancellation mechanism and the idea of linearly-good unknowns, and we use the former idea to deal with the top tangential derivatives and the latter one admitting fast decay rates to control lower-order derivatives.