On the Rayleigh–Taylor instability in compressible viscoelastic fluids

Wang, Weiwei; Zhao, Youyi

doi:10.1016/j.jmaa.2018.03.018

Cited by 17 publications

(6 citation statements)

References 27 publications

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“…In the last decades, this phenomenon has been extensively investigated from mathematical, physical and numerical aspects, see [3,11,48] for examples. It has been also widely investigated how the RT instability evolves under the effects of other physical factors, such as elasticity [18,30,31,49], rotation [3,4], internal surface tension [12,22,53], magnetic fields [24,26,28,29,50,51] and so on.…”

Section: Introductionmentioning

confidence: 99%

Instability of the Abstract Rayleigh--Taylor Problem and Applications

Jiang

Zhan

2018

Preprint

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We prove the existence of a unique unstable strong solution in the sense of L 1 -norm for an abstract Rayleigh-Taylor (RT) problem arising from stratified viscous fluids in Lagrangian coordinates based on a bootstrap instability method. In the proof, we develop a method to modify the initial data of the linearized abstract RT problem based on an existence theory of unique solution of stratified (steady) Stokes problem and an iterative technique, so that the obtained modified initial data satisfy necessary compatibility conditions of the (original) abstract RT problem. Applying an inverse transformation of Lagrangian coordinates to the obtained unstable solution, and then taking proper values of parameters, we can further get unstable solutions for the RT problems in viscoelastic fluids, magnetohydrodynamics (MHD) fluids with zero resistivity and pure viscous fluids (with or without interface intension) in Eulerian coordinates. Our results can be also extended to the corresponding inhomogeneous case (without interface).

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Section: Introductionmentioning

confidence: 99%

Instability of the Abstract Rayleigh--Taylor Problem and Applications

Jiang

Zhan

2018

Preprint

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“…Meshkov and Abarzhi theoretically and experimentally studied the RT flows by focusing of the effect of acceleration on disorder and order in RT mixing [54]. Wang and Zhao mathematically investigated the RTI in the presence of a bounded uniform gravitational field based on Oldroyd-B model inside a compressible viscoelastic fluid [55]. Su uses a sign-changing Taylor sign coefficients for proving the existence of water waves via the method that strong Taylor sign holds in starting time while breaks down at a later time and vice versa [56].…”

Section: Review Of the Current Statusmentioning

confidence: 99%

Plasma Waves and Rayleigh–Taylor Instability: Theory and Application

Singh¹,

Vidhani²,

Yogi³

et al. 2023

Plasma Science - Recent Advances, New Perspectives and Applications

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The presence of plasma density gradient is one of the main sources of Rayleigh–Taylor instability (RTI). The Rayleigh–Taylor instability has application in meteorology to explain cloud formations and in astrophysics to explain finger formation. It has wide applications in the inertial confinement fusion to determine the yield of the reaction. The aim of the chapter is to discuss the current status of the research related to RTI. The current research related to RTI has been reviewed, and general dispersion relation has been derived under the thermal motion of electron. The perturbed densities of ions and electrons are determined using two fluid approach under the small amplitude of oscillations. The dispersion equation is derived with the help of Poisson’s equation and solved numerically to investigate the effect of various parameters on the growth rate and real frequency. It has been shown that the real frequency increases with plasma density gradient, electron temperature and the wavenumber, but magnetic field has opposite effect on it. On the other hand, the growth rate of instability increases with magnetic field and density gradient, but it decreases with electron temperature and wave number.

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“…Firstly, in Sect. 2, we construct linear unstable solutions to the linearized VRT problem; this can be achieved by the modified variational method as in [12,18,38,42]. Secondly, in Sect.…”

Section: (ω) Infmentioning

confidence: 99%

On classical solutions of Rayleigh–Taylor instability in inhomogeneous viscoelastic fluids

Tan

Wang

2019

Bound Value Probl

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We study the nonlinear Rayleigh-Taylor (RT) instability of an inhomogeneous incompressible viscoelastic fluid in a bounded domain. It is well known that there exist strong solutions of RT instability in H 2-norm in inhomogeneous incompressible viscoelastic fluids, when the elasticity coefficient κ is less than some threshold κ C. In this paper, we prove the existence of classical solutions of RT instability in L 1-norm in Lagrangian coordinates based on a bootstrap instability method with finer analysis, if κ < κ C. Moreover, we also get classical solutions of RT instability in L 1-norm in Eulerian coordinates by further applying an inverse transformation of Lagrangian coordinates.

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On the Rayleigh–Taylor instability in compressible viscoelastic fluids

Cited by 17 publications

References 27 publications

Instability of the Abstract Rayleigh--Taylor Problem and Applications

Instability of the Abstract Rayleigh--Taylor Problem and Applications

Plasma Waves and Rayleigh–Taylor Instability: Theory and Application

On classical solutions of Rayleigh–Taylor instability in inhomogeneous viscoelastic fluids

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