Global well-posedness of the short-pulse and sine-Gordon equations in energy space

Details Global well-posedness of the short-pulse and sine-Gordon equations in energy space Global well-posedness of the short-pulse and sine-Gordon equations in energy space

2008-09-30

arxiv.org/abs/0809.5052v2

Commun. Part. Diff. Eq. 35 (2010) 613-629

Mathematics

Analysis of PDEs

17 pages, revised version

Scientific paper

10.1080/03605300903509104

We prove global well-posedness of the short-pulse equation with small initial data in Sobolev space $H^2$. Our analysis relies on local well-posedness results of Sch\"afer & Wayne, the correspondence of the short-pulse equation to the sine-Gordon equation in characteristic coordinates, and a number of conserved quantities of the short-pulse equation. We also prove local and global well-posedness of the sine-Gordon equation in an appropriate function space.

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