Abstract
AbstractWe prove that the recently introduced spin Benjamin–Ono equation admits a Lax pair and deduce a family of conservation laws that allow proving global wellposedness in all Sobolev spaces $H^{k}$
H
k
for every integer $k\geq 2$
k
≥
2
. We also infer an additional family of matrix-valued conservation laws of which the previous family is just the traces.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
Reference3 articles.
1. Berntson, B., Langmann, E., Lenells, J.: Spin generalizations of the Benjamin–Ono equation. arXiv:2201.07269v1
2. Gérard, P., Kappeler, T.: On the integrability of the Benjamin–Ono equation on the torus. Commun. Pure Appl. Math. 74, 1685–1747 (2021)
3. Lecture Notes in Math.;T. Kato,1993
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