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<p>We are concerned with the boundary layer problem for steady relativistic Boltzmann equation in half-space. By introducing some special test functions and choosing suitable estimate orders, we derive a crucial bound on the macroscopic part <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10955_2025_3421_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textbf{P}f\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold">P</mi> <mi>f</mi> </mrow> </math></EquationSource> </InlineEquation>. Under certain admissible conditions and assuming exponential decay for the source term, we demonstrate the existence, continuity and the exponential spacial decay of a boundary layer solution for both linear and nonlinear steady relativistic Boltzmann equations with hard potential collision kernel. The uniqueness is also established under specific constraint conditions.</p>

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The Steady Relativistic Boltzmann Equation in Half-Space

  • 期刊论文

  • 发表日期：

    2025年4月10日

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  • Jing Ouyang,
  • Changguo Xiao

摘要

We are concerned with the boundary layer problem for steady relativistic Boltzmann equation in half-space. By introducing some special test functions and choosing suitable estimate orders, we derive a crucial bound on the macroscopic part \(\textbf{P}f\) P f . Under certain admissible conditions and assuming exponential decay for the source term, we demonstrate the existence, continuity and the exponential spacial decay of a boundary layer solution for both linear and nonlinear steady relativistic Boltzmann equations with hard potential collision kernel. The uniqueness is also established under specific constraint conditions.