Global Solutions for the Gravity Water Waves Equation in Dimension
نویسندگان
چکیده
We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L related norms, with dispersive estimates, which give decay in L∞. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.
منابع مشابه
m at h . A P ] 2 9 Ju n 20 09 GLOBAL SOLUTIONS FOR THE GRAVITY WATER WAVES EQUATION IN DIMENSION
We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L 2 related norms, with dispersive estimates, which give decay in L ∞. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.
متن کاملGlobal solutions for the gravity water waves equation in dimension 3
We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L related norms, with dispersive estimates, which give decay in L∞. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.
متن کاملThe Lifespan of Small Data Solutions in Two Dimensional Capillary Water Waves
This article is concerned with the incompressible, irrotational infinite depth water wave equation in two space dimensions, without gravity but with surface tension. We consider this problem expressed in position-velocity potential holomorphic coordinates, and prove that small data solutions have at least cubic lifespan while small localized data leads to global solutions.
متن کاملVariational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves
The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...
متن کاملSolution of propagation of acoustic-gravity waves in the atmosphere using finite difference method of order two
Investigating waves propagation’s equation in the atmosphere is one of the important and widely used issues in various sciences, which has attracted many researchers. A type of propagating waves is an acoustic-gravity wave. These type of waves have a lot of stationarity properties and can be propagate to a high altitude in the atmosphere. The equation of acoustic-gravity wave propagation is a h...
متن کامل