Examines solution persistence in weighted Sobolev spaces, suggesting space dependence on initial data.
We study persistence properties of the solution of the Benjamin-Ono equation in weighted Sobolev spaces. Roughly, we show that for β<7/2, the solution $u(x,t)$ of the BO remains in the space L²(|x|2β dx) if and only if its data $u(x,0)$ belongs to this space and it is regular enough, i.e. u₀∈ Hβ(R).
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Linares et al. (2026) studied this question.
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