for . Differentiating with respect to
, integrating by parts and using Equation (29
) leads to the
conclusion that the energies
are decaying. Combining this observation with Sobolev embedding leads
to the conclusion that, regardless of the choice of
,
is bounded to the future. Consequently,
regardless of the choice of
,
does not grow faster than linearly to the future. Inserting this
information into Equation (29
) and integrating yields two smooth functions
and
such that
http://www.livingreviews.org/lrr-2010-2 |
Living Rev. Relativity 13, (2010), 2
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