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Yifei Wu

Publications and source records attributed to Yifei Wu.

At least 73 records · Page 4Linked to original sources

Optimal convergence of a second order low-regularity integrator for the KdV equation

In this paper, we establish the optimal convergence result of a second order exponential-type integrator from (136, Numer. Math., 2017) for solving the KdV equation under rough initial data. The scheme is explicit and efficient to implement. By rigorous error analysis, we show that the scheme provides the second order accuracy in $H^γ$ for initial data in $H^{γ+4}$ for any $γ\geq0$, where the regularity requirement is lower than the classical methods. The result is confirmed by numerical experiments and comparisons are made with the Strang splitting scheme.

math.NA↗

Optimal small data Scattering for the generalized derivative nonlinear Schrödinger equations

In this work, we consider the following generalized derivative nonlinear Schrödinger equation \begin{align*} i\partial_t u+\partial_{xx} u +i |u|^{2σ}\partial_x u=0, \quad (t,x)\in \mathbb R\times \mathbb R. \end{align*} We prove that when $σ\ge 2$, the solution is global and scattering when the initial data is small in $H^s(\mathbb R)$, $\frac 12\leq s\leq1$. Moreover, we show that when $0<σ<2$, there exist a class of solitary wave solutions $\{ϕ_c\}$ satisfying $$ \|ϕ_c\|_{H^1(\mathbb R)}\to 0, $$ when $c$ tends to some endpoint, which is against the small data scattering statement. Therefore, in this model, the exponent $σ\ge2$ is optimal for small data scattering. We remark that this exponent is larger than the short range exponent and the Strauss exponent.

math.AP↗

Analysis of misinformation during the COVID-19 outbreak in China: cultural, social and political entanglements

COVID-19 resulted in an infodemic, which could erode public trust, impede virus containment, and outlive the pandemic itself. The evolving and fragmented media landscape is a key driver of the spread of misinformation. Using misinformation identified by the fact-checking platform by Tencent and posts on Weibo, our results showed that the evolution of misinformation follows an issue-attention cycle, pertaining to topics such as city lockdown, cures, and preventions, and school reopening. Sources of authority weigh in on these topics, but their influence is complicated by peoples' pre-existing beliefs and cultural practices. Finally, social media has a complicated relationship with established or legacy media systems. Sometimes they reinforce each other, but in general, social media may have a topic cycle of its own making. Our findings shed light on the distinct characteristics of misinformation during the COVID-19 and offer insights into combating misinformation in China and across the world at large.

cs.SI↗

Orbital stability of solitary waves for derivative nonlinear Schrödinger equation

In this paper, we show the orbital stability of solitons arising in the cubic derivative nonlinear Schrodinger equations. We consider the zero mass case that is not covered by earlier works [8, 3]. As this case enjoys L^2 scaling invariance, we expect the orbital stability in the sense up to scaling symmetry, in addition to spatial and phase translations. For the proof, we are based on the variational argument and extend a similar argument in [21]. Moreover, we also show a self-similar type blow up criteria of solutions with the critical mass 4π.

math.AP↗

Global rough solution for $L^2$-critical semilinear heat equation in the negative Sobolev space

In this paper, we consider the Cauchy global problem for the $L^2$-critical semilinear heat equations $\partial_t h=Δh\pm |h|^{\frac4d}h, $ with $h(0,x)=h_0$, where $h$ is an unknown real function defined on $ \R^+\times\R^d$. In most of the studies on this subject, the initial data $h_0$ belongs to Lebesgue spaces $L^p(\R^d)$ for some $p\ge 2$ or to subcritical Sobolev space $H^{s}(\R^d)$ with $s>0$. We here prove that there exists some positive constant $\varepsilon_0$ depending on $d$, such that the Cauchy problem is locally and globally well-posed for any initial data $h_0$ which is radial, supported away from origin and in the negative Sobolev space $\dot H^{-\varepsilon_0}(\R^d)$ including $L^p(\R^d)$ with certain $p<2$ as subspace. Furthermore, unconditional uniqueness, and $L^2$-estimate both as time $t\to0$ and $t\to +\infty$ were considered.

math.AP↗

Large global solutions for nonlinear Schrödinger equations III, energy-supercritical cases

In this work, we mainly focus on the energy-supercritical nonlinear Schrödinger equation, $$ i\partial_{t}u+Δu= μ|u|^p u, \quad (t,x)\in \mathbb{R}^{d+1}, $$ with $μ=\pm1$ and $p>\frac4{d-2}$. %In this work, we consider the energy-supercritical cases, that is, $p\in (\frac4{d-2},+\infty)$. We prove that for radial initial data with high frequency, if it is outgoing (or incoming) and in rough space $H^{s_1}(\mathbb{R}^d)$ $(s_1<s_c)$ or its Fourier transform belongs to $W^{s_2,1}(\mathbb{R}^d)$ $(s_2<s_c)$, the corresponding solution is global and scatters forward (or backward) in time. We also construct a class of large global and scattering solutions starting with many bubbles, which are mingled with in the physical space and separate in the frequency space. The analogous results are also valid for the energy-subcritical cases.

math.AP↗

A Convolutional Neural Network for Aspect Sentiment Classification

With the development of the Internet, natural language processing (NLP), in which sentiment analysis is an important task, became vital in information processing.Sentiment analysis includes aspect sentiment classification. Aspect sentiment can provide complete and in-depth results with increased attention on aspect-level. Different context words in a sentence influence the sentiment polarity of a sentence variably, and polarity varies based on the different aspects in a sentence. Take the sentence, 'I bought a new camera. The picture quality is amazing but the battery life is too short.'as an example. If the aspect is picture quality, then the expected sentiment polarity is 'positive', if the battery life aspect is considered, then the sentiment polarity should be 'negative'; therefore, aspect is important to consider when we explore aspect sentiment in the sentence. Recurrent neural network (RNN) is regarded as a good model to deal with natural language processing, and RNNs has get good performance on aspect sentiment classification including Target-Dependent LSTM (TD-LSTM) ,Target-Connection LSTM (TC-LSTM) (Tang, 2015a, b), AE-LSTM, AT-LSTM, AEAT-LSTM (Wang et al., 2016).There are also extensive literatures on sentiment classification utilizing convolutional neural network, but there is little literature on aspect sentiment classification using convolutional neural network. In our paper, we develop attention-based input layers in which aspect information is considered by input layer. We then incorporate attention-based input layers into convolutional neural network (CNN) to introduce context words information. In our experiment, incorporating aspect information into CNN improves the latter's aspect sentiment classification performance without using syntactic parser or external sentiment lexicons in a benchmark dataset from Twitter but get better performance compared with other models.

cs.CL↗

Instability of the solitary wave solutions for the genenalized derivative Nonlinear Schrödinger equation in the critical frequency case

We study the stability theory of solitary wave solutions for the generalized derivative nonlinear Schrödinger equation $$ i\partial_{t}u+\partial_{x}^{2}u+i|u|^{2σ}\partial_x u=0. $$ The equation has a two-parameter family of solitary wave solutions of the form \begin{align*} ϕ_{ω,c}(x)=φ_{ω,c}(x)\exp{\big\{ i\frac c2 x-\frac{i}{2σ+2}\int_{-\infty}^{x}φ^{2σ}_{ω,c}(y)dy\big\}}. \end{align*} Here $ φ_{ω,c}$ is some real-valued function. It was proved in \cite{LiSiSu1} that the solitary wave solutions are stable if $-2\sqrt{ω}<c <2z_0\sqrt{ω}$, and unstable if $2z_0\sqrt{ω}<c <2\sqrt{ω}$ for some $z_0\in(0,1)$. We prove the instability at the borderline case $c =2z_0\sqrt{ω}$ for $1<σ<2$, improving the previous results in \cite{Fu-16-DNLS} where $3/2<σ<2$.

math.AP↗

Instability of the standing waves for the nonlinear Klein-Gordon equations in one dimension

In this paper, we consider the following nonlinear Klein-Gordon equation \begin{align*} \partial_{tt}u-Δu+u=|u|^{p-1}u,\qquad t\in \mathbb{R},\ x\in \mathbb{R}^d, \end{align*} with $1<p< 1+\frac{4}{d}$. The equation has the standing wave solutions $u_ω=e^{iωt}ϕ_ω$ with the frequency $ω\in(-1,1)$, where $ϕ_ω$ obeys \begin{align*} -Δϕ+(1-ω^2)ϕ-ϕ^p=0. \end{align*} It was proved by Shatah (1983), and Shatah, Strauss (1985) that there exists a critical frequency $ω_c\in (0,1)$ such that the standing waves solution $u_ω$ is orbitally stable when $ω_c<|ω|<1$, and orbitally unstable when $|ω|<ω_c$. Further, the critical case $|ω|=ω_c$ in the high dimension $d\ge 2$ was considered by Ohta, Todorova (2007), who proved that it is strongly unstable, by using the virial identities and the radial Sobolev inequality. The one dimension problem was left after then. In this paper, we consider the one-dimension problem and prove that it is orbitally unstable when $|ω|=ω_c$.

math.AP↗

Global small solutions to the compressible 2D magnetohydrodynamic system without magnetic diffusion

This paper establishes the global existence and uniqueness of smooth solutions to the two-dimensional compressible magnetohydrodynamic system when the initial data is close to an equilibrium state. In addition, explicit large-time decay rates for various Sobolev norms of the solutions are also obtained. These results are achieved through a new approach of diagonalizing a system of coupled linearized equations. The standard method of diagonalization via the eigenvalues and eigenvectors of the matrix symbol is very difficult to implement here. This new process allows us to obtain an integral representation of the full system through explicit kernels. In addition, in order to overcome various difficulties such as the anisotropicity and criticality, we fully exploit the structure of the integral representation and employ extremely delicate Fourier analysis and associated estimates.

math.AP↗

Stability of multi-solitons for the derivative nonlinear Schr{ö}dinger equation

The nonlinear Schr{ö}dinger equation with derivative cubic nonlinearity admits a family of solitons, which are orbitally stable in the energy space. In this work, we prove the orbital stability of multi-solitons configurations in the energy space, under suitable assumptions on the speeds and frequencies of the composing solitons. The main ingredients of the proof are modulation theory, energy coercivity and monotonicity properties.

math.AP↗

Global well-posedness for periodic generalized KdV equation

In this paper, we show the global well-posedness for periodic gKdV equations in the space $H^s(\mathbb{T})$, $s\ge \frac12$ for quartic case, and $s> \frac59$ for quintic case. These improve the previous results of I-team in 2004. In particular, the result is sharp for quintic case. The main approaches are the I-method combining with the resonance decomposition developed by Miao et al in 2010, and a bilinear Strichartz estimate in periodic setting.

math.AP↗

Global well-posedness for the nonlinear Schrödinger equation with derivative in energy space

In this paper, we prove that there exists some small $\varepsilon_*>0$, such that the derivative nonlinear Schrödinger equation (DNLS) is global well-posedness in the energy space, provided that the initial data $u_0\in H^1(\mathbb{R})$ satisfies $\|u_0\|_{L^2}<\sqrt{2π}+\varepsilon_*$. This result shows us that there are no blow up solutions whose masses slightly exceed $2π$, even if their energies are negative. This phenomenon is much different from the behavior of nonlinear Schrödinger equation with critical nonlinearity. The technique is a variational argument together with the momentum conservation law. Further, for the DNLS on half-line $\mathbb{R}^+$, we show the blow-up for the solution with negative energy.

math.AP↗

Global small solution to the 2D MHD system with a velocity damping term

This paper studies the global well-posedness of the incompressible magnetohydrodynamic (MHD) system with a velocity damping term. We establish the global existence and uniqueness of smooth solutions when the initial data is close to an equilibrium state. In addition, explicit large-time decay rates for various Sobolev norms of the solutions are also given.

math.AP↗

The Cauchy problem for the two dimensional Euler-Poisson system

The Euler-Poisson system is a fundamental two-fluid model to describe the dynamics of the plasma consisting of compressible electrons and a uniform ion background. In the 3D case Guo first constructed a global smooth irrotational solution by using dispersive Klein-Gordon effect. It has been conjectured that same results should hold in the two-dimensional case. In our recent work, we proved the existence of a family of smooth solutions by constructing the wave operators for the 2D system. In this work we completely settle the 2D Cauchy problem.

math-ph↗