NONDISPERSIVE RADIAL SOLUTIONS TO ENERGY SUPERCRITICAL NON-LINEAR WAVE EQUATIONS, WITH APPLICATIONS By CARLOS E. KENIG and FRANK MERLE
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چکیده
In this paper we establish optimal pointwise decay estimates for non-dispersive (compact) radial solutions to non-linear wave equations in 3 dimensions, in the energy supercritical range. As an application, we show for the full energy supercritical range, in the defocusing case, that if the scale invariant Sobolev norm of a radial solution remains bounded in its maximal interval of existence, then the solution must exist for all times and scatter.
منابع مشابه
Nondispersive radial solutions to energy supercritical non - linear wave equations , with applications ∗
in the range p ≥ 5. We deal with (u0, u1) in the scale invariant space Ḣsp× Ḣp, sp = 3 2 − 2 p−1 . (See Definition 2.7 for the precise definition of solution 2000 MSC number 35L70 The first author was supported in part by NSF grant DMS-0456583. The second one was supported in part by CNRS. Part of this research was carried out during visits of the second author to the University of Chicago and ...
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تاریخ انتشار 2009