arXiv subjects

Huali Zhang

Publications and source records attributed to Huali Zhang.

22 records · Page 2Linked to original sources

arXiv2019

Global well-posedness of cubic fractional Schrödinger equations in one dimension

In this paper, we consider the Cauchy's problem of global existence and scattering behavior of small, smooth, and localized solutions of cubic fractional Schrödinger equations in one dimension, \begin{equation*} \mathrm{i} \partial_t u- (-Δ)^{\fracα{2}} u=c_*|u|^2u, \end{equation*} where $α\in (\frac{1}{3},1), c_* \in \mathbb{R}$. Our work is a generalization of the result due to Ionescu and Pusateri \cite{IP}, where the case $α=\frac{1}{2}$ was considered. The highlight in this paper is to give a modified dispersive estimate in weighted Sobolev spaces for cubic fractional Schrödinger equations, which could be used for $ α\in (\frac{1}{3},1)$. Based on this modified dispersive estimate, we prove the global existence and modified scattering behavior of solutions combining space-time resonance and bootstrap arguments.

math.AP↗

arXiv2019

Global smooth solutions of MHD equations with large data

In this paper, we establish the global existence of smooth solutions of the three-dimensional MHD system for a class of large initial data. Both the initial velocity and magnetic field can be arbitrarily large in the critical norm.

math.AP↗

arXiv2019

Global Large Smooth Solutions for 3-D Hall-magnetohydrodynamics

In this paper, the global smooth solution of Cauchy's problem of incompressible, resistive, viscous Hall-magnetohydrodynamics (Hall-MHD) is studied. By exploring the nonlinear structure of Hall-MHD equations, a class of large initial data is constructed, which can be arbitrarily large in $H^3(\mathbb{R}^3)$. Our result may also be considered as the extension of work of Lei-Lin-Zhou from the second-order semi-linear equations to the second-order quasilinear equations, because the Hall term elevates the Hall-MHD system to the quasilinear level.

math.AP↗

arXiv2019

Single MR Image Super-Resolution via Channel Splitting and Serial Fusion Network

Spatial resolution is a critical imaging parameter in magnetic resonance imaging (MRI). Acquiring high resolution MRI data usually takes long scanning time and would subject to motion artifacts due to hardware, physical, and physiological limitations. Single image super-resolution (SISR), especially that based on deep learning techniques, is an effective and promising alternative technique to improve the current spatial resolution of magnetic resonance (MR) images. However, the deeper network is more difficult to be effectively trained because the information is gradually weakened as the network deepens. This problem becomes more serious for medical images due to the degradation of training examples. In this paper, we present a novel channel splitting and serial fusion network (CSSFN) for single MR image super-resolution. Specifically, the proposed CSSFN network splits the hierarchical features into a series of subfeatures, which are then integrated together in a serial manner. Thus, the network becomes deeper and can deal with the subfeatures on different channels discriminatively. Besides, a dense global feature fusion (DGFF) is adopted to integrate the intermediate features, which further promotes the information flow in the network. Extensive experiments on several typical MR images show the superiority of our CSSFN model over other advanced SISR methods.

cs.CV↗