Abstract
The goal of this work is the high frequency approximation of bounded energy solutions to the equation
(E)
□
u
+
|
u
|
4
u
+
|
u
|
α
−
1
u
=
0
,
(
t
,
x
)
∈
R
t
×
R
x
3
,
where
□
=
∂
t
2
−
▵
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.