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<p>In this paper, we investigate the MHD-wave boundary layer equations in Gevrey function spaces without any structural assumption. Compared with the standard MHD boundary layer equations, the tangential magnetic field equation is transformed from a degenerate parabolic equation to a degenerate hyperbolic equation, which creates some new difficulties. By observing a new type of cancellation mechanism for overcoming the loss derivative degeneracy, we show that the MHD-wave boundary layer equations are well-posed with the Gevrey index up to 4/3 in both two- and three-dimensional spaces.</p>

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Gevrey well-posedness of the MHD-wave boundary layer equations without any structure assumption

  • 期刊论文

  • 发表日期：

    2025年11月20日

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  • Rui Xu,
  • Zhan Xu

摘要

In this paper, we investigate the MHD-wave boundary layer equations in Gevrey function spaces without any structural assumption. Compared with the standard MHD boundary layer equations, the tangential magnetic field equation is transformed from a degenerate parabolic equation to a degenerate hyperbolic equation, which creates some new difficulties. By observing a new type of cancellation mechanism for overcoming the loss derivative degeneracy, we show that the MHD-wave boundary layer equations are well-posed with the Gevrey index up to 4/3 in both two- and three-dimensional spaces.