6 papers
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…
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…
Wave operator for the generalized derivative nonlinear Schrödinger equation
Ruobing Bai, Jia Shen
In this work, we prove the existence of wave operator for the following generalized derivative nonlinear Schrödinger equation \begin{align*} i\partial_t u+\partial_x^2 u +i |u|^{2σ…
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…
Remarks on the almost sure well-posedness for incompressible Navier-Stokes equations with arbitrary regularity
Ruobing Bai, Jia Shen
In this note, we study the random data problem for incompressible Navier-Stokes equations in Euclidean space with arbitrary regularity, using the randomization introduced in \cite{…