# Low regularity conservation laws for the Benjamin–Ono equation

@article{Talbut2018LowRC,
title={Low regularity conservation laws for the Benjamin–Ono equation},
author={Blaine Talbut},
journal={arXiv: Analysis of PDEs},
year={2018}
}
• Blaine Talbut
• Published 3 December 2018
• Mathematics, Physics
• arXiv: Analysis of PDEs
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.
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