August 17, 2025Open Access

Stability of rarefaction wave for relaxed compressible Navier-Stokes equations with density-dependent viscosity

Key Points

The solution approaches a rarefaction wave over time, showcasing its nonlinear stability.
Key evidence includes the time-asymptotic behavior of solutions to the Cauchy problem for these equations.
Energy estimates play a critical role in proving stability and constructing the correction function.
This finding has important theoretical implications for mathematical fluid dynamics and related applications.

Abstract

Abstract This article shows time-asymptotic nonlinear stability of rarefaction wave to the Cauchy problem for the one-dimensional relaxed compressible Navier-Stokes equations with density-dependent viscosity. We prove that the solution to this typical system tends time-asymptotically to the rarefaction wave. For this, we technically construct the correction function S ˆ (x, t) S (x, t), which means that S ± S can be non-zero. The proof is accomplished by virtue of energy estimates.

Stability of rarefaction wave for relaxed compressible Navier-Stokes equations with density-dependent viscosity

Key Points

Abstract

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