Global Regularity for 2d Water Waves with Surface Tension
نویسندگان
چکیده
منابع مشابه
Global Regularity for 2d Water Waves with Surface Tension
We consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of our analysis is to develop a sufficiently robust method (the “quasilinear I-method”) which allows us to deal with stron...
متن کاملRegularity of Traveling Free Surface Water Waves with Vorticity
Abstract. We prove real analyticity of all the streamlines, including the free surface, of a gravityor capillary-gravity-driven steady flow of water over a flat bed, with a Hölder continuous vorticity function, provided that the propagating speed of the wave on the free surface exceeds the horizontal fluid velocity throughout the flow. Furthermore, if the vorticity possesses some Gevrey regular...
متن کاملOn 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...
متن کاملTraveling Waves in Deep Water with Gravity and Surface Tension
This paper is concerned with the simulation of periodic traveling deep-water freesurface water waves under the influence of gravity and surface tension in two and three dimensions. A variety of techniques is utilized, including the numerical simulation of a weakly nonlinear model, explicit solutions of low-order perturbation theories, and the direct numerical simulation of the full water wave e...
متن کاملThe Zero Surface Tension Limit of Two-Dimensional Water Waves
We consider two-dimensional water waves of infinite depth, periodic in the horizontal direction. It has been proven by Wu (in the slightly different nonperiodic setting) that solutions to this initial value problem exist in the absence of surface tension. Recently Ambrose has proven that solutions exist when surface tension is taken into account. In this paper, we provide a shorter, more elemen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Memoirs of the American Mathematical Society
سال: 2018
ISSN: 0065-9266,1947-6221
DOI: 10.1090/memo/1227