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<p>The paper examines the Cauchy problem of the multi-dimensional compressible magnetohydrodynamic (MHD) flows. Under a nonlinear constraint on the initial data, we are able to construct global large solutions of this model in critical Besov spaces. Moreover, we provide an example of initial data satisfying this nonlinear constraint, but the norms of each component of the initial velocity field <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="526_2024_2927_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(u_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>u</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> and magnetic field <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="526_2024_2927_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(B_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>B</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> are large.</p>

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Global large solutions to a multi-dimensional compressible magnetohydrodynamic flows with a nonlinear initial constraint

  • 期刊论文

  • 发表日期：

    2025年2月6日

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  • Ningning Gao,
  • Jiahong Wu,
  • Fuyi Xu

摘要

The paper examines the Cauchy problem of the multi-dimensional compressible magnetohydrodynamic (MHD) flows. Under a nonlinear constraint on the initial data, we are able to construct global large solutions of this model in critical Besov spaces. Moreover, we provide an example of initial data satisfying this nonlinear constraint, but the norms of each component of the initial velocity field \(u_0\) u 0 and magnetic field \(B_0\) B 0 are large.