Wave equations associated to Liouville systems and constant mean curvature equations

2011/05/21 by Sagun Chanillo, Po-Lam Yung, Po‐Lam Yung +2
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Spectral Theory in Mathematical Physics #math.AP #math.CA #math.DG

paper · pdf · doi:10.48550/arxiv.1105.4295

arxiv created 2011/05/21 · arxiv updated 2011/05/24

Abstract

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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