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Article overview
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Probabilistic well-posedness for supercritical wave equation on $mathbb{T}^3$ | Chenmin Sun
; Bo Xia
; | Date: |
2 Aug 2015 | Abstract: | In this article, we follow the strategies, listed in cite{Burq2011} and
cite{OhPo}, in dealing with supercritical cubic and quintic wave equations, we
obtain that, the equation
egin{equation*}
left{
egin{split}
&(partial^2_t-Delta)u+|u|^{p-1}u=0, 3<p<5
&ig(u,partial_tuig)|_{t=0}=(u_0,u_1)in H^{s} imes
H^{s-1}=:mathcal{H}^s,
end{split}
ight.
end{equation*} is almost surely global well-posed in the sense of Burq and
Tzvetkovcite{Burq2011} for any $sin (frac{p-3}{p-1},1)$. The key point here
is that $frac{p-3}{p-1}$ is much smaller than the critical index
$frac{3}{2}-frac{2}{p-1}$ for $3<p<5$. | Source: | arXiv, 1508.0228 | Services: | Forum | Review | PDF | Favorites |
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