Low regularity conservation laws for the Benjamin-Ono equation

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 $-\frac{1}{2}<s<0$. The conservation laws are obtained from a study of the perturbation determinant associated to the Lax pair of the equation.

11 pages; minor edits