2023
DOI: 10.4310/acta.2023.v231.n1.a2
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Sharp well-posedness results of the Benjamin–Ono equation in $H^s (\mathbb{T}, \mathbb{R})$ and qualitative properties of its solutions

Patrick Gérard,
Thomas Kappeler,
Peter Topalov
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Cited by 10 publications
(6 citation statements)
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“…For periodic initial data, the same approach was pursued by Molinet and Ribaud [21] and Molinet [19,20] implying global well-posedness in L 2 (T). Relying on the integrability of the equation, Gérard et al [4] showed global well-posedness in H s (T) for s > − 1 2 . The same result has also been obtained by Killip et al [15] for periodic as well as non-periodic initial data.…”
Section: Known Resultsmentioning
confidence: 99%
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“…For periodic initial data, the same approach was pursued by Molinet and Ribaud [21] and Molinet [19,20] implying global well-posedness in L 2 (T). Relying on the integrability of the equation, Gérard et al [4] showed global well-posedness in H s (T) for s > − 1 2 . The same result has also been obtained by Killip et al [15] for periodic as well as non-periodic initial data.…”
Section: Known Resultsmentioning
confidence: 99%
“…Proof. Both estimates follow directly from the assumptions on the support of each ϕ i , i ∈ [4], and by Young's and Hölder's inequality.…”
Section: Dyadic Convolution Estimatesmentioning
confidence: 99%
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“…On the other hand, the recent breakthroughs by Gérard, Kappeler, and Topalov [19] in exploring the complete integrability of the BO, they showed BO on the torus is globally wellposed in H s (T) for any s > − 1 2 . It is therefore natural to consider the low regularity ILW convergence problem via its complete integrability.…”
Section: Corollary 15 (Convergence With Respect To the Different Init...mentioning
confidence: 99%