We study the asymptotic decay properties for defocusing semilinear wave equations
in
with pure power nonlinearity. By applying new vector fields to the null hyperplane,
we derive improved time decay of the potential energy, with a consequence that the
solution scatters both in the critical Sobolev space and energy space for all
.
Moreover, combined with Brezis–Gallouet–Wainger-type of logarithmic Sobolev
embedding, we show that the solution decays pointwise with sharp rate
when
and with
rate
for
all
.
This in particular implies that the solution scatters in energy space when
.
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