Type: Article
Publication Date: 2012-01-01
Citations: 39
DOI: https://doi.org/10.1137/110849791
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.