Abstract
We prove scattering of solutions below the energy norm of the nonlinear Klein-Gordon equation in 3D with a defocusing power-type nonlinearity that is superconformal and energy subcritical: this result extends those obtained in the energy class [4, 18, 19] and those obtained below the energy norm under the additional assumption of spherical symmetry [25]. In order to do that, we generate an exponential-type decay estimate in $H^{s}$, $s < 1$, by means of concentration [1] and a low-high frequency decomposition [2, 7]: this is the starting point to prove scattering. On low frequencies, we modify the arguments in [18, 19]; on high frequencies, we use the smoothing effect of the solutions to control the error terms: this, combined with an almost conservation law, allows to prove this decay estimate.
Citation
Soonsik Kwon. Tristan Roy. "Scattering of rough solutions of the nonlinear Klein-Gordon equations in 3D." Adv. Differential Equations 21 (3/4) 333 - 372, March/April 2016. https://doi.org/10.57262/ade/1455805261
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