On the water-wave equations with surface tension
نویسندگان
چکیده
منابع مشابه
On the Water Waves Equations with Surface Tension
The purpose of this article is to clarify the Cauchy theory of the water waves equations as well in terms of regularity indexes for the initial conditions as for the smoothness of the bottom of the domain (namely no regularity assumption is assumed on the bottom). Our main result is that, following the approach developped in [1], after suitable paralinearizations, the system can be arranged int...
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We study dispersive properties of one-dimensional surface waterwaves under surface tension, based on the formulation of the problem as a nonlinear dispersive equation coupled with a transport-type equation. We establish a dispersion estimate on time scales depending on the size of the frequencies. We infer that, if s is large enough, then a solution u of the dispersive equation satisfies local-...
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In this paper, we prove the local well-posedness of the water wave problem with surface tension in the case of finite depth by working in the Eulerian setting. For the flat bottom, as surface tension tends to zero, the solution of the water wave problem with surface tension converges to the solution of the water wave problem without surface tension.
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In this paper we consider a free boundary problem that describes the motion of two viscous incompressible capillary Newtonian fluids. The fluids are separated by an interface that is unknown and has to be determined as part of the problem. Let Ω1(0) ⊂ Rn+1 (n > 1) be a region occupied by a viscous incompressible fluid, fluid1, and letΩ2(0) be the complement of the closure ofΩ1(0) in Rn+1, corre...
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In this paper the effect of surface tension is considered on two two-dimensional waterwave problems involving pairs of immersed bodies. Both models, having fluid of infinite depth, support localized oscillations, or trapped modes, when capillary effects are excluded. The first pair of bodies is surface-piercing whereas the second pair is fully submerged. In the former case it is shown that the ...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2011
ISSN: 0012-7094
DOI: 10.1215/00127094-1345653