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Vortex patches, the Burgers-Hilbert equation, and normal forms

PDE and Applied Math Seminar

Speaker: John Hunter, UCD
Location: 1147 MSB
Start time: Tue, Feb 12 2013, 3:10PM

The Burgers-Hilbert equation arises as a model equation for the motion of a vortex patch or discontinuity in a two-dimensional, inviscid, incompressible fluid flow. It describes the effect of nonlinear steepening on an interface or wave that oscillates at a constant background frequency. For small amplitudes, these oscillations delay wave breaking. We will explain how non-standard normal form methods can be used to prove an enhanced life-span of small smooth solutions of the Burgers-Hilbert equation (in comparison with the inviscid Burgers equation). These normal form methods can be applied to other quasilinear wave equations, for which the Burgers-Hilbert equation provides a useful test case.