Abstract
In this chapter we prove uniqueness, stability and instability theorems for the rest state of heavy isothermal viscous fluids filling a portion of horizontal layer. A new definition, initial data control, of a solution will be introduced. We provide {a priori estimates for a given spatial norm of the difference between a given flow that may be either steady, or unsteady and the rest state, provided the given flow belongs to a suitable regularity class.
Keywords
- Free Surface
- Initial Data
- Free Boundary
- Rest State
- Nonlinear Stability
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© 2011 Springer-Verlag Berlin Heidelberg
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Padula, M. (2011). Isothermal Fluids with Free Boundaries. In: Asymptotic Stability of Steady Compressible Fluids. Lecture Notes in Mathematics(), vol 2024. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21137-9_4
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DOI: https://doi.org/10.1007/978-3-642-21137-9_4
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21136-2
Online ISBN: 978-3-642-21137-9
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