Almost global existence for the nonlinear Klein-Gordon equation in the nonrelativistic limit

Abstract

We study the one-dimensional nonlinear Klein-Gordon (NLKG) equation with a convolution potential, and we prove that solutions with small $H^s$ norm remain small for long times. The result is uniform with respect to $c\ge 1$, which however has to belong to a set of large measure.

Some typos corrected

References in corpus (3)

• A uniformly accurate (UA) multiscale time integrator Fourier pseoduspectral method for the Klein-Gordon-Schrodinger equations in the nonrelativistic limit regime
• Partially strong transparency conditions and a singular localization method in geometric optics
• Almost global existence for the nonlinear Klein-Gordon equation in the nonrelativistic limit

Cited by in corpus (1)

• Almost global existence for the nonlinear Klein-Gordon equation in the nonrelativistic limit