On well-posedness of incompressible two-phase flows with phase transitions: the case of non-equal densities

DOI10.1007/s00028-012-0161-3zbMath1259.35226OpenAlexW2156660142MaRDI QIDQ1935538

Senjo Shimizu, Jan W. Prüss

Publication date: 18 February 2013

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-012-0161-3

zbMATH Keywords

phase transitionswell-posednesssurface tensionmaximal \(L _{p }\)-regularitytwo-phase Navier-Stokes equations

Mathematics Subject Classification ID

Navier-Stokes equations (35Q30) Capillarity (surface tension) for incompressible viscous fluids (76D45) Free boundary problems for PDEs (35R35) Liquid-gas two-phase flows, bubbly flows (76T10)

Related Items

Qualitative Behaviour of Incompressible Two-Phase Flows with Phase Transitions: The Case of Non-Equal Densities ⋮ Preface. Special issue dedicated to Jan Prüss on the occasion of his 65th birthday ⋮ Qualitative behaviour of incompressible two-phase flows with phase transitions: the isothermal case ⋮ Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension ⋮ On the \(\mathcal{R}\)-boundedness for the two phase problem: compressible-incompressible model problem ⋮ Strong solutions to compressible-incompressible two-phase flows with phase transitions ⋮ On Incompressible Two-Phase Flows with Phase Transitions and Variable Surface Tension

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the two-phase Navier-Stokes equations with surface tension
• Three-dimensional conduction-convection problems with change of phase
• Conduction-convection problems with change of phase
• On the closedness of the sum of two closed operators
• On well-posedness of incompressible two-phase flows with phase transitions: the case of equal densities
• Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension
• Functional calculi for linear operators in vector-valued \(L^p\)-spaces via the transference principle
• Existence of analytic solutions for the classical Stefan problem
• Qualitative behaviour of solutions for the two-phase Navier-Stokes equations with surface tension
• Analytic Solutions for the Two-phase Navier-Stokes Equations with Surface Tension and Gravity
• Well-posedness of a Two-phase Flow with Soluble Surfactant
• $H^\infty$-calculus for the sum of non-commuting operators
• On a resolvent estimate of the Stokes system in a half space arising from a free boundary problem for the Navier-Stokes equations
• Stability of Equilibria for the Stefan Problem With Surface Tension
• On the Classical Solvability of the Stefan Problem in a Viscous Incompressible Fluid Flow
• Analytic solutions for a Stefan problem with Gibbs-Thomson correction
• CLASSICAL SOLVABILITY OF THE TWO-PHASE STEFAN PROBLEM IN A VISCOUS INCOMPRESSIBLE FLUID FLOW
• General dynamical sharp-interface conditions for phase transformations in viscous heat-conducting fluids
• $L_p$-Theory for a Class of Non-Newtonian Fluids
• \(L^p\)-theory of the Stokes equation in a half space
• The \(H^\infty\)-calculus and sums of closed operators