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Research Article | Open Access

Vanishing viscosity limit to the planar rarefaction wave for the two-dimensional radiative hydrodynamics

School of Mathematics, Hefei University of Technology, Hefei 230009, China
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Abstract

In this paper, we are concerned with the vanishing viscosity problem in two-dimensional radiative hydrodynamics. We prove that two-dimensional radiative hydrodynamics converge to the planar rarefaction wave solution for the corresponding two-dimensional compressible Euler equations. By introducing a different scaling and identifying cancellations within the flux terms, we establish a new convergence rate with the assistance of detailed energy estimates.

Keywords

Navier-Stokes equationsradiation termplanar rarefaction wavevanishing viscosity
CLC number: 35Q35, 76N10, 35M10

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AIMS Mathematics
Volume 10 Issue 3,
March 2025
Pages 4860-4898
DOI: 10.3934/math.2025223

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Cite this article:
Ren G. Vanishing viscosity limit to the planar rarefaction wave for the two-dimensional radiative hydrodynamics. AIMS Mathematics, 2025, 10(3): 4860-4898. https://doi.org/10.3934/math.2025223

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Received: 14 November 2024
Revised: 12 February 2025
Accepted: 24 February 2025
Published: 15 March 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)