Chenjie Fan

activity

20142026

most citedGlobal well-posedness for the defocusing mass-critical stochastic nonlinear Schrödinger equation on

R

L^{2}

regularity

7 citations · 33 across the 20 of their papers we have counts for

collaborators

22 papers

math.AP2026

On blow up NLS with a multiplicative noise

Chenjie Fan, Junzhe Wang

It is of significant interest to understand whether a noise will speed up or prevent blow up. Under certain nondegenerate conditions, \cite{dD2005Blowup} proved a multiplicative no…

math.AP2025

On a large deviation principle for 1d cubic NLS with optimal decaying data

Chenjie Fan, Feng Ye

In this article, we revisit the work of \cite{garrido2023large}, and prove large deviation principles for more general random initial data for cubic NLS. The Fourier coefficient of…

math.AP2024

A note on minimal mass blow up for inhomogeneous NLS

Chenjie Fan, Shumao Wang

We revisit the work of \cite{raphael2011existence} on the minimal mass blow up solution for $i u_{t} + Δ u = - k (x) ∣ u ∣^{2} u$ , and extend the construction of such a solution to the $k\in C…

math.AP2022★ 1 cited

On decaying properties of nonlinear Schrödinger equations

Chenjie Fan, Gigliola Staffilani, Zehua Zhao

In this paper we discuss quantitative (pointwise) decay estimates for solutions to the 3D cubic defocusing Nonlinear Schrödinger equation with various initial data, deterministic a…

math.AP2022

A note on decay property of nonlinear Schrödinger equations

Chenjie Fan, Zehua Zhao

In this note, we show the existence of a special solution $u$ to defocusing cubic NLS in $3 d$ , which lives in $H^{s}$ for all $s > 0$ , but scatters to a linear solution in a very slo…

math.AP2021

Long time behavior of stochastic NLS with a small multiplicative noise

Chenjie Fan, Weijun Xu, Zehua Zhao

We prove the global space-time bound for the mass critical nonlinear Schrödinger equation perturbed by a small multiplicative noise in dimension three. The associated scattering be…

math.AP2020★ 2 cited

A note on log-log blow up solutions for stochastic nonlinear Schrödinger equations

Chenjie Fan, Yiming Su, Deng Zhang

In this short note, we present a construction for the log-log blow up solutions to focusing mass-critical stochastic nonlinear Schröidnger equations with multiplicative noises. The…

math.AP2020★ 3 cited

On long time behavior for stochastic nonlinear Schrödinger equations with a multiplicative noise

Chenjie Fan, Zehua Zhao

In this article, we study Stochastic mass critical nonlinear Schrödinger equations with a multiplicative noise in 3D with a slight time decay ( $⟨ t ⟩^{- ε}$ ), and prove…

math.AP2020

Construction of $L^{2}$ log-log blowup solutions for the mass critical nonlinear Schrödinger equation

Chenjie Fan, Dana Mendelson

In this article, we study the log-log blowup dynamics for the mass critical nonlinear Schrödinger equation on $R^{2}$ under rough but structured random perturbations at $L…

math.AP2020

Decay estimates for nonlinear Schrödinger equations

Chenjie Fan, Zehua Zhao

In this short note, we present some decay estimates for nonlinear solutions of 3d quintic, 3d cubic and 2d quintic NLS (nonlinear Schrödinger equations).

math.AP2019★ 4 cited

2D-Defocusing Nonlinear Schrödinger Equation with Random Data on Irrational Tori

Chenjie Fan, Yumeng Ou, Gigliola Staffilani +1

We revisit the work of Bourgain on the invariance of the Gibbs measure for the cubic, defocusing nonlinear Schrödinger equation in 2D on a square torus, and we prove the equivalent…

math.AP2019

A Wong-Zakai theorem for the stochastic mass critical NLS

Chenjie Fan, Weijun Xu

We prove a Wong-Zakai theorem for the defocusing mass-critical stochastic nonlinear Schrödinger equation (NLS) on $R$ . The main ingredient are careful mixtures of bootstra…

math.AP2018★ 1 cited

Decay of the stochastic linear Schrödinger equation in $d \geq 3$ with small multiplicative noise

Chenjie Fan, Weijun Xu

We give decay estimates of the solution to the linear Schrödinger equation in dimension $d \geq 3$ with a small noise which is white in time and colored in space. As a consequence,…

math.AP2018★ 2 cited

Subcritical approximations to stochastic defocusing mass-critical nonlinear Schrödinger equation on $R$

Chenjie Fan, Weijun Xu

We show robustness of various truncated and subcritical approximations to the stochastic defocusing mass-critical nonlinear Schrödinger equation (NLS) in dimension $d = 1$ , whose sol…

math.AP2018★ 7 cited

Global well-posedness for the defocusing mass-critical stochastic nonlinear Schrödinger equation on $R$ at $L^{2}$ regularity

Chenjie Fan, Weijun Xu

We prove global existence and stability of solution to the mass-critical stochastic nonlinear Schrödinger equation in $d = 1$ at $L^{2}$ regularity. Our construction starts with the ex…

math.AP2018★ 1 cited

Global well-posedness for the mass-critical stochastic nonlinear Schrödinger equation on $R$ : general $L^{2}$ data

Chenjie Fan, Weijun Xu

We continue our study for the stochastic defocusing mass crtical nonlinear Schrödinger equation with conservative multiplicative noise, and show that it is globally well-posed for…

math.PR2018

Global well-posedness for the mass-critical stochastic nonlinear Schrödinger equation on $R$ : small initial data

Chenjie Fan, Weijun Xu

We prove the global existence of solution to the small data mass critical stochastic nonlinear Schrödinger equation in $d = 1$ . We further show the stability of the solution under pe…

math.AP2016★ 6 cited

On a bilinear Strichartz estimate on irrational tori and some application

Chenjie Fan, Gigliola Staffilani, Hong Wang +1

We prove a bilinear Strichartz type estimate for irrational tori via a decoupling type argument, \cite{bourgain2014proof}, recovering and generalizing the result of \cite{de2006glo…

math.AP2016★ 1 cited

The $L^{2}$ weak sequential convergence of radial mass critical NLS solutions with mass above the ground state

Chenjie Fan

We study the non-scattering $L^{2}$ solution $u$ to the radial mass critical nonlinear Schrödinger equation with mass just above the ground state, and show that there exists a time…

math.AP2016★ 2 cited

On a variational problem related to NLS on Hyperbolic space

Chenjie Fan, Peter Kleinhenz

Motivated by NLS, We study a variational problem on hyperbolic space. In particular, we compute its minimum value and we show the minimizer does not exist

math.AP2015★ 3 cited

Log-log blow up solutions blow up at exactly m points

Chenjie Fan

We study the focusing mass-critical nonlinear Schrödinger equation, and construct certain solutions which blow up at exactly $m$ points according to the log-log law.

math.PR2014

Convergence of eigenvalues to the support of the limiting measure in critical $β$ matrix models

Chenjie Fan, Alice Guionnet, Yuqi Song +1

We consider the convergence of the eigenvalues to the support of the equilibrium measure in the $β$ ensemble models under a critical condition. We show a phase transition phenomeno…

On blow up NLS with a multiplicative noise

On a large deviation principle for 1d cubic NLS with optimal decaying data

A note on minimal mass blow up for inhomogeneous NLS

On decaying properties of nonlinear Schrödinger equations

A note on decay property of nonlinear Schrödinger equations

Long time behavior of stochastic NLS with a small multiplicative noise

A note on log-log blow up solutions for stochastic nonlinear Schrödinger equations

On long time behavior for stochastic nonlinear Schrödinger equations with a multiplicative noise

Construction of L2 log-log blowup solutions for the mass critical nonlinear Schrödinger equation

Decay estimates for nonlinear Schrödinger equations

2D-Defocusing Nonlinear Schrödinger Equation with Random Data on Irrational Tori

A Wong-Zakai theorem for the stochastic mass critical NLS

Decay of the stochastic linear Schrödinger equation in d≥3 with small multiplicative noise

Subcritical approximations to stochastic defocusing mass-critical nonlinear Schrödinger equation on R

Global well-posedness for the defocusing mass-critical stochastic nonlinear Schrödinger equation on R at L2 regularity

Global well-posedness for the mass-critical stochastic nonlinear Schrödinger equation on R: general L2 data

Global well-posedness for the mass-critical stochastic nonlinear Schrödinger equation on R: small initial data

On a bilinear Strichartz estimate on irrational tori and some application

The L2 weak sequential convergence of radial mass critical NLS solutions with mass above the ground state

On a variational problem related to NLS on Hyperbolic space

Log-log blow up solutions blow up at exactly m points

Convergence of eigenvalues to the support of the limiting measure in critical β matrix models

Construction of $L^{2}$ log-log blowup solutions for the mass critical nonlinear Schrödinger equation

Decay of the stochastic linear Schrödinger equation in $d \geq 3$ with small multiplicative noise

Subcritical approximations to stochastic defocusing mass-critical nonlinear Schrödinger equation on $R$

Global well-posedness for the defocusing mass-critical stochastic nonlinear Schrödinger equation on $R$ at $L^{2}$ regularity

Global well-posedness for the mass-critical stochastic nonlinear Schrödinger equation on $R$ : general $L^{2}$ data

Global well-posedness for the mass-critical stochastic nonlinear Schrödinger equation on $R$ : small initial data

The $L^{2}$ weak sequential convergence of radial mass critical NLS solutions with mass above the ground state

Convergence of eigenvalues to the support of the limiting measure in critical $β$ matrix models