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# Mathematical Research Letters

## Volume 28 (2021)

### Number 3

### Low regularity conservation laws for the Benjamin–Ono equation

Pages: 889 – 905

DOI: https://dx.doi.org/10.4310/MRL.2021.v28.n3.a11

#### Author

#### Abstract

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