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Enhanced Lifespan of Smooth Solutions of a Burgers-Hilbert Equation
Published Web Location
https://arxiv.org/pdf/1112.0813.pdfNo data is associated with this publication.
Abstract
We consider an initial value problem for a quadratically nonlinear inviscid Burgers-Hilbert equation that models the motion of vorticity discontinuities. We use a normal form transformation, which is implemented by means of a near-identity coordinate change of the independent spatial variable, to prove the existence of small, smooth solutions over cubically nonlinear time-scales. For vorticity discontinuities, this result means that there is a cubically nonlinear time-scale before the onset of filamentation.