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arXiv · 1112.0813

Enhanced Lifespan of Smooth Solutions of a Burgers-Hilbert Equation

John Hunter·Mihaela Ifrim
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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.

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John Hunter, Mihaela Ifrim. 2011-12-05. Enhanced Lifespan of Smooth Solutions of a Burgers-Hilbert Equation. https://arxiv.org/abs/1112.0813

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