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- ROWAN KILLIP, XIAOYI ZHANG
- 2008

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iut +∆u = ±|u| 4/d u for large spherically symmetric L 2 x (R d) initial data in dimensions d ≥ 3. In the focusing case we require that the mass is strictly less than that of the ground state. As a consequence, we obtain that in the focusing… (More)

- XIAOYI ZHANG
- 2006

We consider the minimal mass m 0 required for solutions to the mass-critical nonlinear Schrödinger (NLS) equation iut + ∆u = µ|u| 4/d u to blow up. If m 0 is finite, we show that there exists a minimal-mass solution blowing up (in the sense of an infinite spacetime norm) in both time directions, whose orbit in L 2 x (R d) is compact after quotienting out by… (More)

- TERENCE TAO, XIAOYI ZHANG
- 2008

We establish global well-posedness and scattering for solutions to the defocusing mass-critical (pseudoconformal) nonlinear Schrödinger equation iut + ∆u = |u| 4/n u for large spherically symmetric L 2 x (R n) initial data in dimensions n ≥ 3. After using the reductions in [32] to reduce to eliminating blowup solutions which are almost periodic modulo… (More)

- Shancheng Zhao, Xiao Ma, Xiaoyi Zhang, Baoming Bai
- IEEE Trans. Communications
- 2013

- XIAOYI ZHANG
- 2005

We undertake a comprehensive study of the nonlinear Schrödinger equation iut + ∆u = λ 1 |u| p 1 u + λ 2 |u| p 2 u, where u(t, x) is a complex-valued function in spacetime Rt × R n x , λ 1 and λ 2 are nonzero real constants, and 0 < p 1 < p 2 ≤ 4 n−2. We address questions related to local and global well-posedness, finite time blowup, and asymptotic… (More)

- Rowan Killip, Dong Li, Monica Visan, Xiaoyi Zhang
- SIAM J. Math. Analysis
- 2009

Let d ≥ 4 and let u be a global solution to the focusing mass-critical nonlinear Schrödinger equation iut + ∆u = −|u| 4 d u with spherically symmetric H 1 x initial data and mass equal to that of the ground state Q. We prove that if u does not scatter then, up to phase rotation and scaling, u is the solitary wave e it Q. Combining this result with that of… (More)

- ROWAN KILLIP, XIAOYI ZHANG
- 2006

We consider the defocusing ˙ H 1-critical nonlinear Schrödinger equation in all dimensions (n ≥ 3) with a quadratic potential V (x) = ± 1 2 |x| 2. We show global well-posedness for radial initial data obeying ∇u 0 (x), xu 0 (x) ∈ L 2. In view of the potential V , this is the natural energy space. In the repulsive case, we also prove scattering. We follow… (More)

- Junchang Xin, Guoren Wang, Lei Chen, Xiaoyi Zhang, Zhenhua Wang
- DASFAA
- 2007

- Ming-Chun Huang, Jason J. Liu, Wenyao Xu, Nabil Alshurafa, Xiaoyi Zhang, Majid Sarrafzadeh
- IEEE Journal of Biomedical and Health Informatics
- 2014

Physical rehabilitation is an important process for patients recovering after surgery. In this paper, we propose and develop a framework to monitor on-bed range of motion exercises that allows physical therapists to evaluate patient adherence to set exercise programs. Using a dense pressure sensitive bedsheet, a sequence of pressure maps are produced and… (More)

- DONG LI, XIAOYI ZHANG
- 2008

We consider a nonlocal aggregation equation with non-linear diffusion which arises from the study of biological aggrega-tion dynamics. As a degenerate parabolic problem, we prove the well-posedness, continuation criteria and smoothness of local solutions. For compactly supported nonnegative smooth initial data we prove that the gradient of the solution… (More)