Details

Autor(en) / Beteiligte

• Wang, Yanjin
• Tice, Ian
• Kim, Chanwoo

Titel

The Viscous Surface-Internal Wave Problem: Global Well-Posedness and Decay

Ist Teil von

• Archive for rational mechanics and analysis, 2014-04, Vol.212 (1), p.1-92

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2014

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a general rigid bottom in a three-dimensional horizontally periodic setting. We establish the global well-posedness of the problem both with and without surface tension. We prove that without surface tension the solution decays to the equilibrium state at an almost exponential rate; with surface tension, we show that the solution decays at an exponential rate. Our results include the case in which a heavier fluid lies above a lighter one, provided that the surface tension at the free internal interface is above a critical value, which we identify. This means that sufficiently large surface tension stabilizes the Rayleigh–Taylor instability in the nonlinear setting. As a part of our analysis, we establish elliptic estimates for the two-phase stationary Stokes problem.