Classical Solutions of Rayleigh–Taylor instability for inhomogeneous incompressible viscous fluids in bounded domains

We study the existence of unstable classical solutions of the Rayleigh–Taylor instability problem (abbr. RT problem) of an inhomogeneous incompressible viscous fluid in a bounded domain. We find that, by using an existence theory of (steady) Stokes problem and an iterative technique, the initial dat...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2024-05, Vol.63 (4), Article 92
Main Authors: Jiang, Fei, Zhao, Youyi
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Fluid flow
Incompressible flow
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Systems Theory
Taylor instability
Theoretical
Viscous fluids
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Summary:We study the existence of unstable classical solutions of the Rayleigh–Taylor instability problem (abbr. RT problem) of an inhomogeneous incompressible viscous fluid in a bounded domain. We find that, by using an existence theory of (steady) Stokes problem and an iterative technique, the initial data of classical solutions of the linearized RT problem can be modified to new initial data, which can generate local-in-time classical solutions of the RT problem, and are close to the original initial data. Thus, we can use a classical bootstrap instability method to further obtain classical solutions of (nonlinear) RT instability based on the ones of linear RT instability.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-024-02714-8