Invariant Measures and Long-Time Behavior for the Benjamin–Ono Equation

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An optimal regularity result on the quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schr\"odinger equation (2017, background): “quence, we have the following estimate; given t∈ Rand r>0, there exists C= C(t,r) >0 such that ρs,N,r,t(ΨN(t)(A)) ≤ Cρs,N,r,t(A) (3.15) for any N∈ Nand any measurable set A⊂ L2(T). Proof. As in [44, 45, 43, 32], the main idea of the proof of Lemma 3.8 is to reduce the analysis to that at t= 0 ”
On the Integrability of the Benjamin‐Ono Equation on the Torus (2019, background): “3 in [31] on the recurrence of solutions extends in the sense that for any initial datum u.”