Low regularity conservation laws for the Benjamin-Ono equation
classification
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conservationequationlawsbenjamin-onoregularityassociatedcircleconserved
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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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