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Research Article | Open Access

Linear Rayleigh-Taylor instability for compressible viscoelastic fluids

School of Mathematics, Northwest University, Xi'an 710127, China
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Abstract

In this paper, we consider the linear Rayleigh-Taylor instability of an equilibrium state of 3D gravity-driven compressible viscoelastic fluid with the elasticity coefficient κ is less than a critical number κ c in a moving horizontal periodic domain. We first construct the maximal growing mode solutions to the linearized equations by studying a family of modified variational problems, and then we prove an estimate for arbitrary solutions to the linearized equations.

Keywords

linear Rayleigh-Taylor instabilitycompressible viscoelastic fluidmoving domain
CLC number: 35R35, 76E17

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AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 14894-14918
DOI: 10.3934/math.2023761

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Liu C. Linear Rayleigh-Taylor instability for compressible viscoelastic fluids. AIMS Mathematics, 2023, 8(7): 14894-14918. https://doi.org/10.3934/math.2023761

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Received: 16 December 2022
Revised: 09 April 2023
Accepted: 13 April 2023
Published: 15 July 2023
©2023 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)