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Isothermal Fluids with Free Boundaries

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2024)

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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Correspondence to Mariarosaria Padula .

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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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