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March/April 2016 Scattering of rough solutions of the nonlinear Klein-Gordon equations in 3D
Soonsik Kwon, Tristan Roy
Adv. Differential Equations 21(3/4): 333-372 (March/April 2016).

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

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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.

Information

Published: March/April 2016
First available in Project Euclid: 18 February 2016

zbMATH: 1337.35135
MathSciNet: MR3461297

Subjects:
Primary: 35Q55

Rights: Copyright © 2016 Khayyam Publishing, Inc.

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Vol.21 • No. 3/4 • March/April 2016
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