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arXiv · 2606.21208

Spectral analysis of the classical Rayleigh-Taylor instability with an upper free surface

Blake Barker·Tien-Tai Nguyen·Benjamin Settle
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Abstract

In this note, we are interested in the linear Rayleigh-Taylor instability problem for the incompressible fluid with an upper free surface. Using the spectral theory of self-adjoint and compact operator, we rigorously prove the existence of infinitely many normal mode solutions to the linearized equations. Some numerical computations are presented to support our theoretical study.

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Blake Barker, Tien-Tai Nguyen, Benjamin Settle. 2026-06-19. Spectral analysis of the classical Rayleigh-Taylor instability with an upper free surface. https://arxiv.org/abs/2606.21208

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