Threshold phenomenon for the quintic wave equation in three dimensions

For the critical focusing wave equation $\square u=u^5$ on $\mathbb{R}^{3+1}$ in the radial case, we establish the role of the “center stable” manifold $\Sigma$ constructed in [18] near the ground state $(W,0)$ as a threshold between blowup and scattering to zero, establishing a conjecture going back to numerical work by Bizo´n, Chmaj, Tabor [3]. The underlying topology is stronger than the energy norm.


Published in:
Communications in Mathematical Physics, 327, 1, 309-332
Year:
2014
Publisher:
Springer Verlag
ISSN:
0010-3616
Keywords:
Laboratories:




 Record created 2012-10-15, last modified 2018-03-13

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