On the free boundary problem to the two viscous immiscible fluids

DOI10.1016/j.jde.2009.11.001zbMath1189.35390OpenAlexW2053296391MaRDI QIDQ2269626

Zhifei Zhang, Li Xu

Publication date: 17 March 2010

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

Full work available at URL: https://doi.org/10.1016/j.jde.2009.11.001

zbMATH Keywords

free boundary problemnonstationary Navier-Stokes equationsLagrangian coordinatesSobolev-Slobodetski space

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Capillarity (surface tension) for incompressible viscous fluids (76D45) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Free boundary problems for PDEs (35R35)

Related Items (13)

The compressible viscous surface-internal wave problem: stability and vanishing surface tension limit ⋮ On the existence for the free interface 2D Euler equation with a localized vorticity condition ⋮ On a viscous two-fluid channel flow including evaporation ⋮ The Compressible Viscous Surface-Internal Wave Problem: Local Well-Posedness ⋮ On the local existence of the free-surface Euler equation with surface tension ⋮ Almost exponential decay of periodic viscous surface waves without surface tension ⋮ Global solvability of a free boundary three-dimensional incompressible viscoelastic fluid system with surface tension ⋮ The viscous surface-internal wave problem: global well-posedness and decay ⋮ Unnamed Item ⋮ Some Free Boundary Problem for Two-Phase Inhomogeneous Incompressible Flows ⋮ On the local existence and uniqueness for the 3D Euler equation with a free interface ⋮ Global existence and exponential stability for the compressible Navier-Stokes equations with discontinuous data ⋮ A regularity result for the incompressible Euler equation with a free interface

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