On nonlinear rayleigh-taylor instabilities

B. Desjardins; E. Grenier

doi:10.1007/s10114-005-0559-8

On nonlinear rayleigh-taylor instabilities

B. Desjardins^*, E. Grenier

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Some of the mathematical properties of the interface between two incompressible inviscid and immiscible fluids with different densities under the influence of a constant gravity field g are investigated. The purpose of this paper is to prove that linearly unstable modes for Rayleigh-Taylor instabilities give birth to nonlinear instabilities for the full nonlinear system. The main ingredient is a general instability theorem in an analytic framework which enables us to go from linear to nonlinear instabilities.

Original language	English
Pages (from-to)	1007-1016
Number of pages	10
Journal	Acta Mathematica Sinica, English Series
Volume	22
Issue number	4
DOIs	https://doi.org/10.1007/s10114-005-0559-8
Publication status	Published - Jul 2006
Externally published	Yes

Keywords

Analytic regularity
Fluid Mechanics
Instability
Nonlinear
Spectrum

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10.1007/s10114-005-0559-8

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AB - Some of the mathematical properties of the interface between two incompressible inviscid and immiscible fluids with different densities under the influence of a constant gravity field g are investigated. The purpose of this paper is to prove that linearly unstable modes for Rayleigh-Taylor instabilities give birth to nonlinear instabilities for the full nonlinear system. The main ingredient is a general instability theorem in an analytic framework which enables us to go from linear to nonlinear instabilities.

KW - Analytic regularity

KW - Fluid Mechanics

KW - Instability

KW - Nonlinear

KW - Spectrum

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JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

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On nonlinear rayleigh-taylor instabilities

Abstract

Keywords

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