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Global stability of the compressible viscous surface waves in an infinite layer

Guilong Gui and Zhifei Zhang
Vol. 7 (2025), No. 3, 535–593
DOI: 10.2140/paa.2025.7.535
Abstract

We consider the global stability of the compressible viscous surface waves in the absence of surface tension effect with steady-state configurations and the reference domain being the horizontal infinite layer. The fluid dynamics are governed by the three-dimensional gravity-driven isentropic compressible Navier–Stokes equations. We develop a new mathematical approach to establish global well-posedness of free boundary problems of the multidimensional compressible Navier–Stokes system based on the Lagrangian framework, which requires no compatibility conditions on the initial data.

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Keywords
compressible viscous surface waves, Lagrangian coordinates, global well-posedness, steady-state
Mathematical Subject Classification
Primary: 35Q30, 35R35, 76E19, 76N10
Milestones
Received: 16 April 2024
Revised: 7 April 2025
Accepted: 12 May 2025
Published: 18 June 2025
Authors
Guilong Gui
School of Mathematics and Computational Science
Xiangtan University
Xiangtan
China
Zhifei Zhang
School of Mathematical Sciences
Peking University
Beijing
China
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