On the Rayleigh-Taylor instability for the two coupled fluids

Yiping Meng; Yiping Meng

doi:10.3934/math.20241572

AIMS Mathematics

2024, Volume 9, Issue 11: 32849-32871. doi: 10.3934/math.20241572

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Research article

On the Rayleigh-Taylor instability for the two coupled fluids

Yiping Meng ^,

School of science, Jiangsu University of Science and Technology, Zhenjiang 212003, China

Received: 14 September 2024 Revised: 22 October 2024 Accepted: 01 November 2024 Published: 20 November 2024
MSC : 76E25, 76E17, 76W05, 35Q35

In this paper, we considered the Rayleigh-Taylor (RT) instability for two incompressible, immisicible, invisid coupled fluids, which were Euler and magnetohydrodynamic with zero resistivity. Under the action of the uniform gravitational field, the two fluids interacted at a free interface. We utilized the flow map to denote the Lorentz force under the Lagrangian coordinates. We first showed the ill-posedness to the linear problem around the RT steady state solution. By virtue of such an ill-posed result, we showed that the nonlinear system is also ill-posed.
- two coupled fluids,
- RT instability,
- incompressible fluids
Citation: Yiping Meng. On the Rayleigh-Taylor instability for the two coupled fluids[J]. AIMS Mathematics, 2024, 9(11): 32849-32871. doi: 10.3934/math.20241572

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Abstract

In this paper, we considered the Rayleigh-Taylor (RT) instability for two incompressible, immisicible, invisid coupled fluids, which were Euler and magnetohydrodynamic with zero resistivity. Under the action of the uniform gravitational field, the two fluids interacted at a free interface. We utilized the flow map to denote the Lorentz force under the Lagrangian coordinates. We first showed the ill-posedness to the linear problem around the RT steady state solution. By virtue of such an ill-posed result, we showed that the nonlinear system is also ill-posed.

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