7 papers
Pathwise Alignment for Collaborative Filtering: Bilateral Conditional Flow Regularization
Zhiwei Li, Guodong Long, Chengqi Zhang +1
Collaborative filtering predicts user-item interactions from implicit feedback. We focus on matrix factorization (MF) trained with the Bayesian Personalized Ranking loss. This loss…
Global theory for NLS in the weighted spaces II: final data problem
Yujin Guo, Jia Shen, Yifei Wu +1
In this paper, we study the final data problem for the defocusing nonlinear Schrödinger equation (NLS) in weighted spaces $\dotΣ^s(\mathbb…
Modified wave operators for nonlinear Schrödinger equations in the full subcritical long range regime
Jia Shen, Yifei Wu
We construct modified wave operators for the nonlinear Schrödinger equation in the full subcritical long-range case , with small, nonvanish…
The subsonic limit of the 3D Zakharov system
Rui Jia, Jia Shen, Yifei Wu
We obtain the optimal convergence rates in the subsonic limit of the three-dimensional Zakharov system for initial data belonging to the low-regularity Sobolev space $\HH^s=H^s\tim…
Optimal error bounds on the exponential wave integrator for nonlinear Schrödinger equations with highly singular potential
Weizhu Bao, Chushan Wang, Yifei Wu
We establish error estimates of the first-order exponential wave integrator (EWI) for the nonlinear Schrödinger equation (NLSE) with a highly singular potential in w…
Global well-posedness for the defocusing 3D quadratic NLS in the sharp critical space
Jia Shen, Yifei Wu
In this paper, we prove the global well-posedness of defocusing 3D quadratic nonlinear Schrödinger equation \begin{align*} i\partial_t u + \frac12Δu = |u| u, \end{align*} in its sh…
Scattering for defocusing mass sub-critical NLS
Jia Shen, Yifei Wu
In this paper, we consider the -scattering of defocusing mass sub-critical nonlinear Schrödinger equations with low weighted initial condition. It is known that the scatteri…