Zobrazeno 1 - 10
of 116
pro vyhledávání: '"Fan, Chenjie"'
We continue our study of bilinear estimates on waveguide $\mathbb{R}\times \mathbb{T}$ started in \cite{DFYZZ2024,Deng2023}. The main point of the current article is, comparing to previous work \cite{Deng2023}, that we obtain estimates beyond the sem
Externí odkaz:
http://arxiv.org/abs/2407.05654
We prove dispersive decay, pointwise in time, for solutions to the mass-critical nonlinear Schr\"odinger equation in spatial dimensions $d=1,2,3$.
Externí odkaz:
http://arxiv.org/abs/2403.09989
Autor:
Fan, Chenjie, Wang, Shumao
We revisit the work of \cite{raphael2011existence} on the minimal mass blow up solution for $iu_{t}+\Delta u=-k(x)|u|^{2}u$, and extend the construction of such a solution to the $k\in C^{2}$ case.
Comment: 21 pages, comments are welcome
Comment: 21 pages, comments are welcome
Externí odkaz:
http://arxiv.org/abs/2402.12135
We study local-in-time and global-in-time bilinear Strichartz estimates for the Schr\"odinger equation on waveguides. As applications, we apply those estimates to study global well-posedness of nonlinear Schr\"odinger equations on these waveguides.
Externí odkaz:
http://arxiv.org/abs/2402.02916
We study the linear profile decomposition for the Airy type equation, where the associated Strichartz inequality corresponds to the Fourier extension inequality on the odd curve $\xi^{\ell}$. We also investigate an inhomogeneous case, modeled by the
Externí odkaz:
http://arxiv.org/abs/2306.13311
In this paper we discuss quantitative (pointwise) decay estimates for solutions to the 3D cubic defocusing Nonlinear Schr\"odinger equation with various initial data, deterministic and random. We show that nonlinear solutions enjoy the same decay rat
Externí odkaz:
http://arxiv.org/abs/2211.03124
Autor:
Fan, Chenjie, Zhao, Zehua
In this note, we show the existence of a special solution $u$ to defocusing cubic NLS in $3d$, which lives in $H^{s}$ for all $s>0$, but scatters to a linear solution in a very slow way. We prove for this $u$, for all $\epsilon>0$, one has $\sup_{t>0
Externí odkaz:
http://arxiv.org/abs/2203.06896
We prove the global space-time bound for the mass critical nonlinear Schr\"odinger equation perturbed by a small multiplicative noise in dimension three. The associated scattering behavior are also obtained. We also prove a global Strichartz space-ti
Externí odkaz:
http://arxiv.org/abs/2111.07212
Autor:
Fan, Chenjie, Liang, Qingyuan, Wang, Yan, Chen, Peimei, Wu, Jiakai, Wu, Qingnan, Jiang, Shijun, Zhou, Yang, He, Rui, Tai, Fuju
Publikováno v:
In Science of the Total Environment 15 June 2024 929
In this short note, we present a construction for the log-log blow up solutions to focusing mass-critical stochastic nonlinear Schr\"oidnger equations with multiplicative noises. The solution is understood in the sense of controlled rough path as in
Externí odkaz:
http://arxiv.org/abs/2011.12171