Long time Solutions for a Burgers-Hilbert Equation via a Modified Energy Method
- Author(s): Hunter, John K.
- Ifrim, Mihaela
- Tataru, Daniel
- Wong, Tak Kwong
- et al.
Published Web Locationhttps://arxiv.org/pdf/1301.1947.pdf
We consider an initial value problem for a quadratically nonlinear inviscid Burgers-Hilbert equation that models the motion of vorticity discontinuities. We use a modified energy method to prove the existence of small, smooth solutions over cubically nonlinear time-scales.