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<p>We consider a model of two-dimensional isentropic compressible Navier–Stokes equations, where the classical Newtonian flow is replaced by the Maxwell flow. We demonstrate the asymptotic stability of planar rarefaction waves for this model, provided that the initial perturbations and wave amplitudes are sufficiently small. The main result is proved by using basic <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2467_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> energy methods, and some new cancellations are crucial for closing the energy estimates.</p>

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Asymptotic stability of planar rarefaction waves for two-dimensional hyperbolized compressible Navier–Stokes equations

  • 期刊论文

  • 发表日期：

    2025年4月3日

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  • Lukang Yan,
  • Lan Zhang

摘要

We consider a model of two-dimensional isentropic compressible Navier–Stokes equations, where the classical Newtonian flow is replaced by the Maxwell flow. We demonstrate the asymptotic stability of planar rarefaction waves for this model, provided that the initial perturbations and wave amplitudes are sufficiently small. The main result is proved by using basic \(L^{2}\) L 2 energy methods, and some new cancellations are crucial for closing the energy estimates.