Abstract :
The goal of this work is the high frequency approximation of bounded energy solutions to the
equation
u + |u|4u + |u|α−1u = 0, (t,x) ∈ Rt ×R3x
, (E)
where = ∂2
t
− x is the wave operator and α is a real number, 1 < α <5. We prove that the
description of Bahouri and Gérard [Amer. J. Math. 121 (1999) 131–175] about the critical case still
holds for Eq. (E) locally in time.
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