Wave equations associated to Liouville systems and constant mean curvature equations

Details Wave equations associated to Liouville systems and constant mean curvature equations Wave equations associated to Liouville systems and constant mean curvature equations

2011-05-21

arxiv.org/abs/1105.4295v1

Mathematics

Analysis of PDEs

Scientific paper

We study the wave analog of the Liouville equation and the constant mean
curvature equations in 2 space dimensions, which are energy critical. We
exhibit a blow-up criteria for the former using tools from conformal geometry,
and we exhibit finite time blow-up for the latter under suitable assumptions on
the initial data.

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