SCATTERING OF ROUGH SOLUTIONS OF THE NONLINEAR KLEIN-GORDON EQUATIONS IN 3D

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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.
Publisher
KHAYYAM PUBL CO INC
Issue Date
2016-03
Language
English
Article Type
Article
Keywords

SCHRODINGER-EQUATIONS; ENERGY SCATTERING; WELL-POSEDNESS; CAUCHY-PROBLEM; TIME DECAY; WAVE; OPERATORS; SPACE

Citation

ADVANCES IN DIFFERENTIAL EQUATIONS, v.21, no.3-4, pp.333 - 372

ISSN
1079-9389
URI
http://hdl.handle.net/10203/207938
Appears in Collection
MA-Journal Papers(저널논문)
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