On the two-phase navier-stokes equations with surface tension
Gottfried Anger,Gieri Simonett +1 more
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In this paper, the Navier-Stokes free boundary problem is considered in a situation where the initial interface is close to a halfplane and the fluids are separated by an interface that is unknown and has to be determined as part of the problem.Citations
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Local well-posedness of the viscous surface wave problem without surface tension
TL;DR: In this paper, the authors consider a viscous fluid of finite depth below the air, occupying a three-dimensional domain bounded below by a fixed solid boundary and above by a free moving boundary.
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Decay of viscous surface waves without surface tension
TL;DR: In this paper, a local well-posedness theory of the Navier-Stokes equations in the presence of a moving boundary and a two-tier energy method were proposed to solve the long time behavior of a free surface with small amplitude.
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Decay of viscous surface waves without surface tension in horizontally infinite domains
TL;DR: In this paper, the authors consider the case in which the free interface is horizontally infinite and prove that the problem is globally well-posed and that solutions decay to equilibrium at an algebraic rate.
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The Viscous Surface-Internal Wave Problem: Global Well-Posedness and Decay
Yanjin Wang,Ian Tice,Chanwoo Kim +2 more
TL;DR: In this paper, the authors considered 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.
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Qualitative behaviour of solutions for the two-phase Navier–Stokes equations with surface tension
TL;DR: In this paper, the two-phase free boundary value problem for the isothermal Navier-Stokes system is studied for general bounded geometries in absence of phase transitions, external forces and boundary contacts.
References
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Book
Theory of function spaces
TL;DR: In this article, the authors measure smoothness using Atoms and Pointwise Multipliers, Wavelets, Spaces on Lipschitz Domains, Wavelet and Sampling Numbers.
Book
Interpolation Spaces: An Introduction
Jöran Bergh,Jörgen Löfström +1 more
TL;DR: In this paper, the authors define the Riesz-Thorin Theorem as a necessary and sufficient condition for interpolation spaces, and apply it to approximate spaces in the context of vector spaces.