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In this paper we give sufficient conditions for the stability of the standing waves of least energy for nonlinear Klein-Gordon equations.
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… (More)
In this paper we derive estimates to the free boundary problem for the Euler equation with surface tension, and without surface tension provided the Rayleigh-Taylor sign condition holds. We prove… (More)
We establish a sharp instability theorem for the bound states of lowest energy of the nonlinear Klein-Gordon equation,utt−◃u+f(u)=0, and the nonlinear Schrödinger equation, −iut−◃u+f(u)=0.
In this paper we prove the instability of the ground state, i.e. least energy steady-state solution of nonlinear Klein-Gordon equations with space dimension n » 3. 0. Introduction. We present here a… (More)