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

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.

17 pages, revised version

References in corpus (2)

• The short pulse equation is integrable
• Solitary wave solutions of the short pulse equation

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