Geodesic
On the low regularity phase space of the Benjamin–Ono equation
Patrick Gérard1 orcid ; Petar Topalov2 orcid
1Université Paris-Saclay, Orsay, France
2Northeastern University, Boston, USA
EMS surveys in mathematical sciences, Tome 12 (2025) no. 1, pp. 185-214

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DOI

In this paper, we prove that the Benjamin–Ono equation is globally in time C0-well-posed in the Hilbert space H−1/2,log​(T,R) of periodic distributions in H−1/2(T,R) with log​-weights. The space H−1/2,log​(T,R) can thus be considered as a maximal low regularity phase space for the Benjamin–Ono equation corresponding to the scale Hs(T,R), s>−1/2.
DOI : 10.4171/emss/88
Classification : 37K15, 47B35
Mots-clés : Benjamin–Ono equation, well-posedness, logarithmic estimates

Patrick Gérard  1   ; Petar Topalov  2

1 Université Paris-Saclay, Orsay, France
2 Northeastern University, Boston, USA 
Patrick Gérard; Petar Topalov. On the low regularity phase space of the Benjamin–Ono equation. EMS surveys in mathematical sciences, Tome 12 (2025) no. 1, pp. 185-214. doi: 10.4171/emss/88
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