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# Global existence of weak solutions for the Burgers–Hilbert equation

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.

Paper:
Available as PDF (320 Kbytes).
Author(s):
Alberto Bressan
Khai T. Nguyen
Submitted by:
; 2014-02-17.