Enhanced Lifespan of Smooth Solutions of a Burgers-Hilbert Equation

Details Enhanced Lifespan of Smooth Solutions of a Burgers-Hilbert Equation Enhanced Lifespan of Smooth Solutions of a Burgers-Hilbert Equation

2011-12-05

arxiv.org/abs/1112.0813v1

Mathematics

Analysis of PDEs

13 pages, 1 figure

Scientific paper

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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