Searcharxiv⌕ Search

arXiv subjects

Ze Li

Publications and source records attributed to Ze Li.

54 records · Page 3Linked to original sources
arXiv2021

Global Schrödinger map flows to Kähler manifolds with small data in critical Sobolev spaces: Energy critical case

In this paper and the companion work \cite{LIZE2}, we prove that the Schrödinger map flows from $\Bbb R^d$ with $d\ge 2$ to compact Kähler manifolds with small initial data in critical Sobolev spaces are global. The main difficulty compared with the constant sectional curvature case is that the gauged equation now is not self-contained due to the curvature part. Our main idea is to use a novel bootstrap-iteration scheme to reduce the gauged equation to an approximate constant curvature system in finite times of iteration. This paper with the companion work \cite{LIZE2} solves the open problem raised by Tataru.

math.AP↗
arXiv2021

Magnetic and magnetocaloric properties of melt-extracted Mn1.26Fe0.60P0.48Si0.52 microwires

The polycrystalline Mn1.26Fe0.60P0.48Si0.52 microwires were successfully fabricated for the first time by the melt-extraction technique, and their magnetic and magnetocaloric properties were investigated systematically. The structural analysis shows that the microwires possess a hexagonal phase with Fe2P type, with a homogeneous composition distribution. Magnetometry measurements show that the microwires undergo a weak first-order magnetic phase transition at a temperature of 142 K. The maximum magnetic entropy change of the microwires reaches 4.64 Jkg-1K-1 for a field change of 5 T. These low-cost Mn1.26Fe0.60P0.48Si0.52 microwires are promising for active magnetic refrigeration in the liquid nitrogen temperature range.

physics.app-ph↗
arXiv2021

Polarized hyperspectral imaging with single fiber bundle via incoherent light transmission matrix approach

The scattering of multispectral incoherent light is a common and unfavorable signal scrambling in natural scenes. However, the blurred light spot due to scattering still holds lots of information remaining to be explored. Former methods failed to recover the polarized hyperspectral information from scattered incoherent light or relied on additional dispersion elements. Here we put forward the transmission matrix (TM) approach for extended objects under incoherent illumination by speculating the unknown TM through experimentally calibrated or digitally emulated ways. Employing a fiber bundle as a powerful imaging and dispersion element, we recover the spatial information in 252 polarized-spectral channels from a single speckle, thus achieving single-shot, high-resolution, broadband hyperspectral imaging for two polarization states with the cheap, compact, fiber-bundle-only system. Based on the scattering principle itself, our method not only greatly improves the robustness of the TM approach to retrieve the input spectral information, but also reveals the feasibility to explore the polarized spatio-spectral information from blurry speckles only with the help of simple optical setups.

eess.IV↗
arXiv2020

On global dynamics of Schrödinger map flows on hyperbolic planes near harmonic maps

The results of this paper are twofold: In the first part, we prove that for Schrödinger map flows from hyperbolic planes to Riemannian surfaces with non-positive sectional curvatures, the harmonic maps which are holomorphic or anti-holomorphic of arbitrary size are asymptotically stable. In the second part, we prove that for Schrödinger map flows from hyperbolic planes into Kähler manifolds, the admissible harmonic maps of small size are asymptotically stable. The asymptotic stability results stated here contain two types: one is the convergence in $L^{\infty}_x$ as the previous works, the other is convergence to harmonic maps plus radiation terms in the energy space, which is new in literature of Schrödinger map flows without symmetry assumptions.

math.AP↗
arXiv2020

Asymptotic stability of solitons to 1D Nonlinear Schrodinger Equations in subcritical case

In this paper, we prove the asymptotic stability of solitary waves to 1D nonlinear Schrödinger equations in the subcritical case with symmetry and spectrum assumptions. One of the main ideas is to use the vector fields method developed by Cuccagna, Georgiev, Visciglia to overcome the weak decay with respect to $t$ of the linearized equation caused by the one dimension setting and the weak nonlinearity caused by the subcritical growth of the nonlinearity term. Meanwhile, we apply the polynomial growth of the high Sobolev norms of solutions to 1D Schrödinger equations obtained by Staffilani to control the high moments of the solutions emerging from the vector fields method.

math.AP↗
arXiv2020

Global Schrödinger map flows to Kähler manifolds with small data in critical Sobolev spaces: High dimensions

In this paper, we prove that the Schrödinger map flows from $\Bbb R^d$ with $d\ge 3$ to compact Kähler manifolds with small initial data in critical Sobolev spaces are global. This is a companion work of our previous paper [23] where the energy critical case $d=2$ was solved. In the first part of this paper, for heat flows from $\Bbb R^d$ ($d\ge 3$) to Riemannian manifolds with small data in critical Sobolev spaces, we prove the decay estimates of moving frame dependent quantities in the caloric gauge setting, which is of independent interest and may be applied to other problems. In the second part, with a key bootstrap-iteration scheme in our previous work [23], we apply these decay estimates to the study of Schrödinger map flows by choosing caloric gauge. This work with our previous work solves the open problem raised by Tataru.

math.AP↗
arXiv2019

Asymptotic stability of harmonic maps between 2D hyperbolic spaces under the wave map equation. II. Small energy case

In this paper, we prove that the small energy harmonic maps from $\Bbb H^2$ to $\Bbb H^2$ are asymptotically stable under the wave map equation in the subcritical perturbation class. This result may be seen as an example supporting the soliton resolution conjecture for geometric wave equations without equivariant assumptions on the initial data. In this paper, we construct Tao's caloric gauge in the case when nontrivial harmonic map occurs. With the "dynamic separation" the master equation of the heat tension field appears as a semilinear magnetic wave equation. By the endpoint and weighted Strichartz estimates for magnetic wave equations obtained by the first author \cite{Lize1}, the asymptotic stability follows by a bootstrap argument.

math.AP↗
arXiv2018

Endpoint Strichartz estimates for magnetic wave equations on two dimensional hyperbolic spaces

In this paper, we prove that Kato smoothing effects for magnetic Schrödinger operators can yield the endpoint Strichartz estimates for linear wave equation with magnetic potential on two dimensional hyperbolic spaces. This result serves as a cornerstone for the author's work \cite{Lize} and collaborative work \cite{LMZ} in the study of asymptotic stability of harmonic maps for wave maps from $\Bbb R\times\Bbb H^2$ to $\Bbb H^2$.

math.AP↗
arXiv2017

Propagation of moments and uniqueness of weak solutions to the Vlasov-Poisson-Fokker-Planck system

In this paper, we prove the uniqueness of weak solutions to the Vlasov-Poisson-Fokker-Planck system in $C([0,T]; L^p)$, by assuming the solution has a local bounded density which tends to infinite with a "reasonable" rate as $t\to 0$. And particularly as a corollary, we get the uniqueness of weak solutions with initial data $f_0$ satisfying $f_0|v|^2\in L^1$, which solves the uniqueness of weak solutions with finite energy. In addition, we prove that the moments with respect to the velocity propagate for any order higher than 2.

math.AP↗
arXiv2017

Convergence to harmonic maps for the Landau-Lifshitz flows on two dimensional hyperbolic spaces

In this paper, we prove that the solution of the Landau-Lifshitz flow $u(t,x)$ from $\mathbb{H}^2$ to $\mathbb{H}^2$ converges to some harmonic map as $t\to\infty$. The essential observation is that although there exist infinite numbers of harmonic maps from $\Bbb H^2$ to $\Bbb H^2$, the heat flow initiated from $u(t,x)$ for any given $t>0$ converges to the same harmonic map as the heat flow initiated from $u(0,x)$. This observation enables us to construct a variant of Tao's caloric gauge to reduce the convergence to harmonic maps for the Landau-Lifshitz flow to the decay of the corresponding heat tension field. The advantage of the strategy used in this paper is that we can see the limit harmonic map directly by evolving $u(0,x)$ along a heat flow without evolving the Landau-Lifshitz flow to the infinite time.

math.AP↗
arXiv2017

Decay and scattering of solutions to nonlinear Schrödinger equations with regular potentials for nonlinearities of sharp growth

In this paper, we prove the decay and scattering in the energy space for nonlinear Schrödinger equations with regular potentials in $\Bbb R^d$ namely, $i{\partial _t}u + Δu - V(x)u + λ|u|^{p - 1}u = 0$. We will prove decay estimate and scattering of the solution in the small data case when $1+\frac{2}{d}<p\le1+\frac{4}{d-2}$, $d\ge3$. The index $1+\frac{2}{d}$ is sharp for scattering concerning the result of W. Strauss [21].

math.AP↗
arXiv2016

Long time behaviors for 3D cubic damped Klein-Gordon equations in inhomogeneous mediums

In this paper, we study the asymptotic dynamics of global solutions to damped Klein-Gordon equations in inhomogeneous mediums (KGI). In the defocusing case, we prove for any initial data, the solution is globally define in forward time and it will converge to an equilibrium. In the focusing case, for global solutions, we prove the solutions converge to the superposition of equilibriums among which there exists at most one equilibrium to KGI and the other equilibriums are solutions to stationary nonlinear Klein-Gordon equations. The core ingredients of our proof are the existence of the "concentration-compact attractor" and the gradient system theory.

math.AP↗
arXiv2016

Asymptotic behaviors of Landau-Lifshitz flows from $\Bbb R^2$ to Kähler manifolds

In this paper, we study the asymptotic behaviors of finite energy solutions to the Landau-Lifshitz flows from $\Bbb R^2$ into Kähler manifolds. First, we prove that the solution with initial data below the critical energy converges to a constant map in the energy space as $t\to \infty$ for the compact Riemannian surface targets. In particular, when the target is a two dimensional sphere, we prove that the solution to the Landau-Lifshitz-Gilbert equation with initial data having an energy below $4π$ converges to some constant map in the energy space. Second, for general compact Kähler manifolds and initial data of an arbitrary finite energy, we obtain a bubbling theorem analogous to the Struwe's results on the heat flows.

math.AP↗
arXiv2015

Asymptotic decomposition for nonlinear damped Klein-Gordon equations

In this paper, we proved that if the solution to damped focusing Klein-Gordon equations is global forward in time, then it will decouple into a finite number of equilibrium points with different shifts from the origin. The core ingredient of our proof is the existence of the "concentration-compact attractor" which yields a finite number of profiles. Using damping effect, we can prove all the profiles are equilibrium points.

math.AP↗
arXiv2015

Asymptotic Stability of Solitons to Nonlinear Schrodinger Equations on Star Graphs

In this paper, we prove the asymptotic stability of nonlinear Schrodiger equations on star graphs, which partially solves an open problem in D. Noja \cite{DN}. The essential ingredient of our proof is the dispersive estimate for the linearized operator around the soliton with Kirchhoff boundary condition. In order to obtain the dispersive estimates, we use the Born's series technique and scattering theory for the linearized operator.

math.AP↗