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<p>The asymptotic limit of the Navier–Stokes–Korteweg system for barotropic capillary fluids with density-dependent viscosities in the low-Mach number and vanishing viscosity regime is established in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation>, with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(d=2,3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. In the relative energy framework, we prove the convergence of weak solutions of the Navier–Stokes–Korteweg system to the strong solution of the incompressible Euler system. The convergence is obtained through the use of suitable dispersive estimates for an acoustic system altered by the presence of the Korteweg tensor.</p>

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Inviscid incompressible limit for capillary fluids with density-dependent viscosity

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月25日

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  • Matteo Caggio,
  • Donatella Donatelli,
  • Lars Eric Hientzsch

摘要

The asymptotic limit of the Navier–Stokes–Korteweg system for barotropic capillary fluids with density-dependent viscosities in the low-Mach number and vanishing viscosity regime is established in \(\mathbb {R}^d\) R d , with \(d=2,3\) d = 2 , 3 . In the relative energy framework, we prove the convergence of weak solutions of the Navier–Stokes–Korteweg system to the strong solution of the incompressible Euler system. The convergence is obtained through the use of suitable dispersive estimates for an acoustic system altered by the presence of the Korteweg tensor.