Global Well-Posedness of the Short-Pulse and Sine–Gordon Equations in Energy Space Academic Article uri icon

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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 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.

publication date

  • March 16, 2010