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

Guangrong Ren; Guangrong Ren

doi:10.3934/math.2025223

AIMS Mathematics

2025, Volume 10, Issue 3: 4860-4898. doi: 10.3934/math.2025223

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Research article

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

Guangrong Ren ^,

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

Received: 14 November 2024 Revised: 12 February 2025 Accepted: 24 February 2025 Published: 06 March 2025
MSC : 35Q35, 76N10, 35M10

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.
- Navier-Stokes equations,
- radiation term,
- planar rarefaction wave,
- vanishing viscosity
Citation: Guangrong Ren. Vanishing viscosity limit to the planar rarefaction wave for the two-dimensional radiative hydrodynamics[J]. AIMS Mathematics, 2025, 10(3): 4860-4898. doi: 10.3934/math.2025223

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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.

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