Hello, I am Chenjie Fan. I am currently an associate proessor at Academy of Mathematics and System Science, Chinese Academy of Sciences. I obtained my Phd in MIT, 2017, under the supervision of Gigliola Staffilani. After that, I did my postdoc (Dickson Instructor) at Unversity of Chicago, 2017-2020, mentored by Carlos Kenig.
Email: my email can be found in my recent arxiv preprint.
I am mostly interested in nonlinear dispersive PDE, via both determnistic and probalistic approaches. I am a very open mind person and interested in PDE and Analysis related questions. I am also interested in stochastic analysis recently. All my papers can be found in Arxiv, arxiv.org/search/?query=chenjie+fan&searchtype=all&source=header
Research:
Long time behavior of stochastic NLS with a small multiplicative noise, Joint with Weijun Xu and Zehua Zhao, arxiv preprint.
A note on log-log blow up solutions for stochastic nonlinear Schrödinger equations, joint with Yiming Su, Deng Zhang, Stochastics and Partial Differential Equations: Analysis and Computations.
On long time behavior for stochastic nonlinear Schrödinger equations with a multiplicative noise, with Zehua Zhao, submitted.
Construction of L2 log-log blowup solutions for the mass critical nonlinear Schrödinger equation, with Dana Mendelson, to appear in JEMS.
Decay estimates for nonlinear Schrödinger equations, with Zehua Zhao, DCDS
2D-Defocusing Nonlinear Schrödinger Equation with Random Data on Irrational Tori, with Gigliola Staffilani, Yumeng Ou, Hong Wang, Stochastics and Partial Differential Equations: Analysis and Computations.
A Wong-Zakai theorem for the stochastic mass critical NLS, with Weijun Xu, SIMA
Decay of the stochastic linear Schrödinger equation in d\geq 3 with small multiplicative noise, with Weijun Xu, Stochastics and Partial Differential Equations: Analysis and Computations.
Subcritical approximations to stochastic defocusing mass-critical nonlinear Schrödinger equation on R, with Weijun Xu, JDE
Global well-posedness for the defocusing mass-critical stochastic nonlinear Schrödinger equation on
R with L2 regularity, to appear in APDE
On a bilinear Strichartz estimate on irrational tori , with Gigliola Staffilani, Hong Wang, Bobby Wilson, APDE
The L2 weak sequential convergence of radial mass critical NLS solutions with mass above the ground state, IMRN
On a variational problem related to NLS on Hyperbolic space, with Peter Kleinhenz, arxiv preprint,
Log-log blow up solutions blow up at exactly m points, AIHP
Convergence of eigenvalues to the support of the limiting measure in critical \beta matrix models, with
Alice Guionnet, Yuqi Song, Andi Wang, Random Matrices: Theory and Applications
Teaching：
非线性薛定谔方程的爆破解 （blow up of NLS），2020 Spring
I was the lecturer of analysis 1,2.3 for several times during my postdoc time in Chicago. I also taught an ODE class there.
I gave three guest lectures on concentration compactness in 18.155, when I was a student in MIT.
a litte thing about me:
我在读博士后的时候开始特别欣赏范仲淹的岳阳楼记，我一直把他贴在我的办公室。等我开始在数学院工作后，我又特别为司马迁的报任安书所感动。总得来说这是我最喜欢的两篇文章，虽然高中时已经学过，但那时确实不懂。
Some links:
AMSS: http://www.amss.cas.cn
Researchgate page: https://www.researchgate.net/profile/Chenjie-Fan-2