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The Rayleigh–Taylor instability for the Verigin problem with and without phase transition

  • Jan Prüss
  • Gieri Simonett
  • Mathias WilkeEmail author
Article
  • 68 Downloads

Abstract

Isothermal compressible two-phase flows in a capillary are modeled with and without phase transition in the presence of gravity, employing Darcy’s law for the velocity field. It is shown that the resulting systems are thermodynamically consistent in the sense that the available energy is a strict Lyapunov functional. In both cases, the equilibria with flat interface are identified. It is shown that the problems are well-posed in an \(L_p\)-setting and generate local semiflows in the proper state manifolds. The main result concerns the stability of equilibria with flat interface, i.e. the Rayleigh–Taylor instability.

Keywords

Two-phase flows Phase transition Darcy’s law with gravity Available energy Quasilinear parabolic evolution equations Maximal regularity Generalized principle of linearized stability 

Mathematics Subject Classification

35Q35 76D27 76E17 35R37 35K59 

Notes

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institut für MathematikMartin-Luther-Universität Halle-WittenbergHalleGermany
  2. 2.Department of MathematicsVanderbilt UniversityNashvilleUSA

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