Seminari del Dipartimento
Analisi Dynamics of the nonlinear Klein-Gordon equation in the nonrelativistic limit Stefano Pasquali 06-12-2017 - 16:00 Largo San Leonardo Murialdo,1 - Pal.C - AULA 311
We study the the nonlinear Klein-Gordon (NLKG) equation on a manifold $M$ in the nonrelativistic limit (as the speed of light $c o infty$). We consider a higher-order normalized approximation of NLKG (corresponding to the NLS at order $r=1$), and prove that when $M$ is a smooth compact manifold or $R^d$, the solution of the approximating equation approximates the solution of the NLKG locally uniformly in time. When $M=R^d$, $d geq 2$, we prove that for $r geq 2$ small radiation solutions of the order $r$ normalized equation approximate solutions of the nonlinear NLKG up to times of order $cO(c^{2(r-1)})$. |