On a priori estimates and existence of periodic solutions to the modified Benjamin-Ono equation below H1/2 (T)

[摘要] A priori estimates and existence of real-valued periodic solutions to the modified Benjamin-Ono equation with initial data in H-s for s > 1/4 are proved locally in time. The approach relies on frequency dependent time localization, after which dispersive properties from Euclidean space are recovered. The same regularity results are proved for the cubic derivative nonlinear Schrodinger equation. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-25

[关键词] Dispersive equations;A priori estimates;Modified Benjamin-Ono equation;Derivative nonlinear Schrodinger equation;Short-time Fourier restriction norm method