Preprint 2014-004
Global existence of weak solutions for the Burgers–Hilbert equation
Alberto Bressan and Khai T. Nguyen
Abstract: This paper establishes the global existence of weak solutions to the Burgers-Hilbert equation, for general initial data in $L^2(\mathbb{R})$. For positive times, the solution lies in $L^2\cap L^\infty$. A partial uniqueness result is proved for spatially periodic solutions, as long as the total variation remains locally bounded.