On stabilizing effect of elasticity in the Rayleigh–Taylor problem of stratified viscoelastic fluids

Jiang, Fei; Jiang, Song; Wu, Guochun

doi:10.1016/j.jfa.2017.01.007

Cited by 51 publications

(42 citation statements)

References 42 publications

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“…Let us first recall a mathematical model, which describes the horizontally periodic motion of stratified incompressible viscous fluids in an infinity layer domain [21]:…”

Section: Motion Equations In Eulerian Coordinatesmentioning

confidence: 99%

“…In the last decades, this phenomenon has been extensively investigated from mathematical, physical and numerical aspects, see [2,8,29] for instance. It has been also widely investigated how the RT instability evolves under the effects of other physical factors, such as elasticity [3,11,21,23,30], rotation [2,4], (internal) surface tension [9,14,34], magnetic fields [16-20, 22, 31, 32] and so on. In this article, we are interested in the effect of surface tension on the linear RT instability in stratified incompressible viscous fluids.…”

Section: Introductionmentioning

confidence: 99%

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On effects of viscosity and magnetic fields on the largest growth rate of linear Rayleigh–Taylor instability

Jiang

2016

Journal of Mathematical Physics

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We investigate the effect of surface tension on the linear Rayleigh-Taylor (RT) instability in stratified incompressible viscous fluids with or without (interface) surface tension. The existence of linear RT instability solutions with largest growth rate Λ is proved under the instability condition (i.e., the surface tension coefficient ϑ is less than a threshold ϑ c ) by modified variational method of PDEs. Moreover we find a new upper bound for Λ. In particular, we observe from the upper bound that Λ decreasingly converges to zero, as ϑ goes from zero to the threshold ϑ c . The convergence behavior of Λ mathematically verifies the classical RT instability experiment that the instability growth is limited by surface tension during the linear stage.

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“…Let us first recall a mathematical model, which describes the horizontally periodic motion of stratified incompressible viscous fluids in an infinity layer domain [21]:…”

Section: Motion Equations In Eulerian Coordinatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On effects of viscosity and magnetic fields on the largest growth rate of linear Rayleigh–Taylor instability

Jiang

2016

Journal of Mathematical Physics

Self Cite

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“…In the last decades, it has been also widely investigated how the RT instability evolves under the effects of other physical factors, such as elasticity [4,11,27,29,42,46], rotation [3,6,45], internal surface tension [9,16,24,48], magnetic fields [5, 17, 19-23, 25, 26], and so on. We also refer to the other related mathematical problems [1, 12, 13, 30, 32-34, 36, 38, 41].…”

Section: Introductionmentioning

confidence: 99%

“…To begin with, let us recall the RT problem of stratified viscoelastic incompressible fluids in an infinity layer domain [27]:…”

Section: Introductionmentioning

confidence: 99%

On effect of surface tension in the Rayleigh–Taylor problem of stratified viscoelastic fluids

Xiong

2019

Bound Value Probl

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In this article, we investigate the effect of surface tension in the Rayleigh-Taylor (RT) problem of stratified incompressible viscoelastic fluids. We prove that there exists an unstable solution to the linearized stratified RT problem with a largest growth rate Λ under the instability condition (i.e., the surface tension coefficient ϑ is less than a threshold ϑ c). Moreover, for this instability condition, the largest growth rate Λ ϑ decreases from a positive constant to 0, when ϑ increases from 0 to ϑ c , which mathematically verifies that the internal surface tension can constrain the growth of the RT instability during the linear stage.

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“…In this article, we are interested in the RT instability of an inhomogeneous incompressible viscoelastic fluid. The RT instability in viscoelastic fluid has been widely studied, see [15,25,27] for examples. Moreover, the RT instability also has been investigated under other physical factors, such as internal surface tension [12,17,41], magnetic fields [4, 5, 19-21, 23, 24, 39, 40], rotation [3,6,29], and so on.…”

Section: Introductionmentioning

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 stabilizing effect of elasticity in the Rayleigh–Taylor problem of stratified viscoelastic fluids

Cited by 51 publications

References 42 publications

On effects of viscosity and magnetic fields on the largest growth rate of linear Rayleigh–Taylor instability

On effects of viscosity and magnetic fields on the largest growth rate of linear Rayleigh–Taylor instability

On effect of surface tension in the Rayleigh–Taylor problem of stratified viscoelastic fluids

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

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