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arXiv · 0809.5052

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

Dmitry Pelinovsky·Anton Sakovich
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Abstract

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 Schäfer & 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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Dmitry Pelinovsky, Anton Sakovich. 2010-04-27. Global well-posedness of the short-pulse and sine-Gordon equations in energy space. https://doi.org/10.1080/03605300903509104

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