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Decay of viscous
surface waves without surface tension in horizontally
infinite domains
Yan Guo and Ian Tice |
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Vol. 6 (2013), No. 6, 1429–1533
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Abstract |
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We 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. The fluid dynamics are governed by the gravity-driven incompressible Navier–Stokes equations, and the effect of surface tension is neglected on the free surface. The long-time behavior of solutions near equilibrium has been an intriguing question since the work of Beale (1981). This is the second in a series of three papers by the authors that answers the question. Here we consider the case in which the free interface is horizontally infinite; we prove that the problem is globally well-posed and that solutions decay to equilibrium at an algebraic rate. In particular, the free interface decays to a flat surface. Our framework utilizes several techniques, which include
Our decay estimates lead to the construction of global-in-time solutions to the surface wave problem. |
Keywords
Navier–Stokes equations, free boundary problems, global
existence
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Mathematical Subject Classification 2010
Primary: 35Q30, 35R35, 76D03
Secondary: 35B40, 76E17
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Milestones
Received: 15 October 2012
Accepted: 15 November 2012
Published: 18 November 2013
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Authors |
| Yan Guo | |
| Division of Applied
Mathematics Brown University 182 George Street Providence, Rhode Island 02912 USA |
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| Ian Tice | |
| Department of Mathematical
Sciences Carnegie Mellon University Pittsburgh PA 15213 USA |
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