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Long time Solutions for a Burgers-Hilbert Equation via a Modified Energy Method
John K. Hunter, Mihaela Ifrim, Daniel Tataru +1
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 m…
Orientation Waves in a Director Field With Rotational Inertia
Giuseppe Ali, John K. Hunter
We study the propagation of orientation waves in a director field with rotational inertia and potential energy given by the Oseen-Frank energy functional from the continuum theory…
Short-Time Existence for Scale-Invariant Hamiltonian Waves
John K. Hunter
We prove short-time existence of smooth solutions for a class of nonlinear, and in general spatially nonlocal, Hamiltonian evolution equations that describe the self-interaction of…
Diffractive Nonlinear Geometrical Optics for Variational Wave Equations and the Einstein Equations
Giuseppe Ali, John K. Hunter
We derive an asymptotic solution of the vacuum Einstein equations that describes the propagation and diffraction of a localized, large-amplitude, rapidly-varying gravitational wave…