Global well-posedness of the Benjamin–Ono equation in low-regularity spaces

Ionescu, Alexandru¹ ; Kenig, Carlos²

¹ Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Van Vleck Hall, Madison, Wisconsin 53706
² Department of Mathematics, University of Chicago, 5734 University Ave, Chicago, Illinois 60637-1514

Journal of the American Mathematical Society, Tome 20 (2007) no. 3, pp. 753-798

Résumé

We prove that the Benjamin–Ono initial-value problem is globally well-posed in the Banach spaces $H^\sigma _r(\mathbb {R})$, $\sigma \geq 0$, of real-valued Sobolev functions.

Détail

DOI : 10.1090/S0894-0347-06-00551-0

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