Mathematical Research Letters

Volume 28 (2021)

Number 3

Low regularity conservation laws for the Benjamin–Ono equation

Pages: 889 – 905



Blaine Talbut (Department of Mathematics, University of California, Los Angeles, Cal., U.S.A.)


We obtain conservation laws at negative regularity for the Benjamin–Ono equation on the line and on the circle. These conserved quantities control the $H^s$ norm of the solution for $-\frac{1}{2} \lt s \lt 0$. The conservation laws are obtained from a study of the perturbation determinant associated to the Lax pair of the equation.

In the preparation of this paper, the author received support from NSF grants DMS-1500707, DMS-1600942, and DMS-1763074.

Received 13 May 2019

Accepted 7 October 2019

Published 2 June 2021