Long time Solutions for a Burgers-Hilbert Equation via a Modified Energy Method
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Long time Solutions for a Burgers-Hilbert Equation via a Modified Energy Method

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https://arxiv.org/pdf/1301.1947.pdf
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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 modified energy method to prove the existence of small, smooth solutions over cubically nonlinear time-scales.

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