Abstract The Benjamin–Ono equation is shown to be well-posed, both on the line and on the
circle, in the Sobolev spaces H s for s>− 1 2. The proof rests on a new gauge transformation …

We prove that the cubic nonlinear Schrödinger equation (both focusing and defocusing) is
globally well-posed in (see [15, 24, 33, 39]). To overcome the failure of uniform continuity of …

We prove that the Benjamin--Ono equation on the torus is globally in time well-posed in the
Sobolev space $ H^{s}(\mathbb {T},\mathbb {R}) $ for any $ s>-1/2$ and ill-posed for $ s\le …

arxiv:2311.12334v1 [math.AP] 21 Nov 2023 Page 1 arxiv:2311.12334v1 [math.AP] 21 Nov
2023 SCALING-CRITICAL WELL-POSEDNESS FOR CONTINUUM CALOGERO–MOSER …

Global well-posedness for the derivative nonlinear Schrödinger equation in L2.R/ Page 1 ©
2024 European Mathematical Society Published by EMS Press J. Eur. Math. Soc. (Online first) …

We consider the derivative nonlinear Schrödinger equation in one space dimension, posed
both on the line and on the circle. This model is known to be completely integrable and L 2 …

We consider the derivative nonlinear Schrödinger equation in one spatial dimension, which
is known to be completely integrable. We prove that the orbits of bounded and …

Based on the nonlinear steepest descent method of Deift and Zhou for oscillatory Riemann–
Hilbert problems and the Dbar approach, the long‐time asymptotic behavior of solutions to …

We prove low regularity a priori estimates for the derivative nonlinear Schrödinger equation
in Besov spaces with positive regularity index conditional upon small L2-norm. This covers …

Given a suitable solution V (t, x) to the Korteweg–de Vries equation on the real line, we
prove global well-posedness for initial data u (0, x)∈ V (0, x)+ H-1 (R). Our conditions on V …