Low-regularity well-posedness for dispersive equations with derivative nonlinearity and quasi-periodic initial data
Robert Schippa
Abstract
We show low-regularity well-posedness of the Korteweg-de Vries equation with spatially quasi-periodic initial data. To this end, we employ frequency-dependent time localization and a bilinear version of the Córdoba--Fefferman square function estimate to show a bilinear Strichartz estimate for quasi-periodic functions. The solutions are proved to preserve the Sobolev regularity of the initial data, which was not the case in earlier works. The argument extends to other dispersion relations and higher order nonlinearities.
Create a lesson
Related papers
Learning Lyapunov Operators for Nonlinear Systems
Amartya Mukherjee, Maxwell Fitzsimmons, David C. Del Rey Fernández et al.
Existence of Admissible Subsolutions to the Dirichlet Problem for Symmetric Augmented k-Hessian Type Equations in Bounded Domains
Quang Hong Dinh, Bang Van Tran, Ngoan Tien Ha et al.
The Regularity datum on time-varying graph domains and Dirichlet--Regularity duality
Martin Dindoš
Existence of flat blowups at boundary points of anisotropic minimizing hypercurrents
Michael Novack, Reinaldo Resende
Isolated singularities of the capillary equation with negative gravity
Bin Deng, Jiahuan Li, Yilu Liu et al.
Local behavior for solutions to inhomogeneous singular parabolic p-Laplace equations
Xia Hao, Yan Li, Zhiwen Zhao