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Yanqing Wang

Publications and source records attributed to Yanqing Wang.

At least 55 records · Page 3Linked to original sources
arXiv2019

New regularity criteria based on pressure or gradient of velocity in Lorentz spaces for the 3D Navier-Stokes equations

In this paper, we derive regular criteria via pressure or gradient of the velocity in Lorentz spaces to the 3D Navier-Stokes equations. It is shown that a Leray-Hopf weak solution is regular on $(0,T]$ provided that either the norm $\|Π\|_{L^{p,\infty}(0,T; L ^{q,\infty}(\mathbb{R}^{3}))} $ with $ {2}/{p}+{3}/{q}=2$ $({3}/{2}<q<\infty)$ or $\|\nablaΠ\|_{L^{p,\infty}(0,T; L ^{q,\infty}(\mathbb{R}^{3}))} $ with $ {2}/{p}+{3}/{q}=3$ $(1<q<\infty)$ is small. This gives an affirmative answer to a question proposed by Suzuki in [26, Remark 2.4, p.3850]. Moreover, regular conditions in terms of $\nabla u$ obtained here generalize known ones to allow the time direction to belong to Lorentz spaces.

math.AP↗
arXiv2019

New $\varepsilon$-regularity criteria of suitable weak solutions of the 3D Navier-Stokes equations at one scale

In this paper, by invoking the appropriate decomposition of pressure to exploit the energy hidden in pressure, we present some new $\varepsilon$-regularity criteria for suitable weak solutions of the 3D Navier-Stokes equations at one scale: for any $p,q\in [1,\infty]$ satisfying $1\leq 2/q+3/p <2$, there exists an absolute positive constant $\varepsilon$ such that $u\in L^{\infty}(Q(1/2))$ if $$\|u\|_{L^{p,q}(Q(1))}+\|Π\|_{L^{1 }(Q(1))}<\varepsilon.$$ This is an improvement of corresponding results recently proved by Guevara and Phuc in [7, Calc. Var. 56:68, 2017]. As an application of these $\varepsilon$-regularity criteria, we improve the known upper box dimension of the possible interior singular set of suitable weak solutions of the Navier-Stokes system from $975/758(\approx1.286)$ [28] to $2400/1903 (\approx1.261)$.

math.AP↗
arXiv2019

$\varepsilon$-regularity criteria in anisotropic Lebesgue spaces and Leray's self-similar solutions to the 3D Navier-Stokes equations

In this paper, we establish some $\varepsilon$-regularity criteria in anisotropic Lebesgue spaces for suitable weak solutions to the 3D Navier-Stokes equations as follows: $$ \limsup\limits_{\varrho\rightarrow0} \varrho^{1-\frac{2}{p}-\sum\limits^{3}_{j=1}\frac{1}{q_{j}}} \|u\|_{L_{t}^{p}L^{\overrightarrow{q}}_{x}(Q(\varrho))} \leq\varepsilon, ~~\frac{2}{p}+\sum\limits^{3}_{j=1}\frac{1}{q_{j}} \leq2~~~~~\text{with}~q_{j} > 1;\\$$$$ \sup_{-1\leq t\leq0}\|u\|_{L^{\overrightarrow{q}}(B(1))} < \varepsilon,~~\frac{1}{q_{1}}+\frac{1}{q_{2}}+\frac{1}{q_{3}} <2\quad \text{with}\, 1<q_{j}<\infty;$$ $$\|u \|_{L_{t}^{p}L^{\overrightarrow{q}}_{x}(Q(1))} +\|Π\|_{L^{1}(Q(1))}\leq\varepsilon, \quad \frac2p+\sum^{3}_{j=1}\frac{1}{q_{j}} <2 ~~~\text{with}~~ 1<q_{j}<\infty, $$ which extends the previous results in [2, 12, 18, 19, 22, 37, 43]. As an application, in the spirit of [4], we prove that there does not exist a nontrivial Leray's backward self-similar solution with profiles in $L^{\overrightarrow{p}}(\mathbb{R}^{3})$ with $\frac{1}{p_{1}}+\frac{1}{p_{2}}+\frac{1}{p_{3}}<2$. This generalizes the corresponding results of [4, 20, 28, 38].

math.AP↗
arXiv2019

Localizing Discriminative Visual Landmarks for Place Recognition

We address the problem of visual place recognition with perceptual changes. The fundamental problem of visual place recognition is generating robust image representations which are not only insensitive to environmental changes but also distinguishable to different places. Taking advantage of the feature extraction ability of Convolutional Neural Networks (CNNs), we further investigate how to localize discriminative visual landmarks that positively contribute to the similarity measurement, such as buildings and vegetations. In particular, a Landmark Localization Network (LLN) is designed to indicate which regions of an image are used for discrimination. Detailed experiments are conducted on open source datasets with varied appearance and viewpoint changes. The proposed approach achieves superior performance against state-of-the-art methods.

cs.CV↗
arXiv2019

Environmental Remediation Applications of Carbon Nanotube and Graphene Oxide: Adsorption and Catalysis

Environmental issues such as the wastewater have influenced each aspect of our lives. Coupling the existing remediation solutions with exploring new functional carbon nanomaterials (e.g. carbon nanotube, graphene oxide, graphene) by various perspectives shall open up a new venue to understand the environmental issues, phenomenon and find out the ways to get along with the nature. This review makes an attempt to provide an overview of potential environmental remediation solutions to the diverse challenges happening by using low-dimensional carbon nanomaterials and their composites as adsorbents, catalysts or catalysts support towards for the social sustainability.

physics.app-ph↗
arXiv2018

A $\varepsilon$-regularity criterion without pressure of suitable weak solutions to the Navier-Stokes equations at one scale

In this paper, we continue our work in [15] to derive ε-regularity criteria at one scale without pressure for suitable weak solutions to the Navier-Stokes equations. We establish a $\varepsilon$-regularity criterion below of suitable weak solutions, for any $δ>0$, $$\iint_{Q(1)}|u|^{\frac{5}{2}+δ}dxdt\leq \varepsilon.$$ As an application, we extend the previous corresponding results concerning the improvement of the classical Caffarelli--Kohn--Nirenberg theorem by a logarithmic factor.

math.AP↗
arXiv2018

On Wolf's regularity criterion of suitable weak solutions to the Navier-Stokes equations

In this paper, we consider the local regularity of suitable weak solutions to the 3D incompressible Navier-Stokes equations. By means of the local pressure projection introduced by Wolf in [15,16], we present a $\varepsilon$-regularity criterion below of suitable weak solutions $$ \iint_{Q(1)}|u|^{20/7}dxdt\leq \varepsilon, $$ which gives an improvement of previous corresponding results obtained in Chae and Wolf [3, Arch. Ration. Mech. Anal., 225: 549-572, 2017], in Guevara and Phuc [6, Calc. Var., 56:68, 2017] and in Wolf [16, Ann. Univ. Ferrara, 61: 149-171, 2015].

math.AP↗
arXiv2018

Human and Machine Speaker Recognition Based on Short Trivial Events

Trivial events are ubiquitous in human to human conversations, e.g., cough, laugh and sniff. Compared to regular speech, these trivial events are usually short and unclear, thus generally regarded as not speaker discriminative and so are largely ignored by present speaker recognition research. However, these trivial events are highly valuable in some particular circumstances such as forensic examination, as they are less subjected to intentional change, so can be used to discover the genuine speaker from disguised speech. In this paper, we collect a trivial event speech database that involves 75 speakers and 6 types of events, and report preliminary speaker recognition results on this database, by both human listeners and machines. Particularly, the deep feature learning technique recently proposed by our group is utilized to analyze and recognize the trivial events, which leads to acceptable equal error rates (EERs) despite the extremely short durations (0.2-0.5 seconds) of these events. Comparing different types of events, 'hmm' seems more speaker discriminative.

cs.SD↗
arXiv2017

Remarks on the singular set of suitable weak solutions to the 3D Navier-Stokes equations

In this paper, let $\mathcal{S}$ denote the possible interior singular set of suitable weak solutions of the 3D Navier-Stokes equations. We improve the known upper box-counting dimension of this set from $360/277(\approx1.300)$ in [24] to $975/758(\approx1.286)$. It is also shown that $Λ(\mathcal{S},r(\log(e/r))^σ)=0(0\leqσ<27/113)$, which extends the previous corresponding results concerning the improvement of the classical Caffarelli-Kohn-Nirenberg theorem by a logarithmic factor in Choe and Lewis [3, J. Funct. Anal., 175: 348-369, 2000] and in Choe and Yang et al. [4, Comm. Math. Phys, 336: 171-198, 2015]. The proof is inspired by a new $\varepsilon$-regularity criterion proved by Guevara and Phuc in [7, Calc. Var. 56:68, 2017].

math.AP↗
arXiv2017

Time-varying Bang-bang Property of Minimal Controls for Approximately Null-controllable Heat Equations

In this paper, optimal time control problems and optimal target control problems are studied for the approximately null-controllable heat equations. Compared with the existed results on these problems, the boundary of control variables are not constants but time varying functions. The time-varying bang-bang property for optimal time control problem, and an equivalence theorem for optimal control problem and optimal target problem are obtained.

math.OC↗
arXiv2016

On the box-counting dimension of potential singular set for suitable weak solutions to the 3D Navier-Stokes equations

In this paper, we are concerned with the upper box-counting dimension of the set of possible singular points in space-time of suitable weak solutions to the 3D Navier-Stokes equations. By taking full advantage of the pressure $Π$ in terms of $\nabla Π$ in equations, we show that this upper box dimension is at most $135/104(\approx1.30)$, which improves the known upper box-counting dimension $95/63(\approx1.51)$ in Koh et al. [9, J. Differential Equations, 261: 3137--3148, 2016], $45/29(\approx1.55)$ in Kukavica et al. [11, Nonlinearity 25: 2775-2783, 2012] and $135/82(\approx1.65)$ in Kukavica [10, Nonlinearity 22: 2889-2900, 2009].

math.AP↗
arXiv2016

A Numerical Scheme for BSVIEs

In this paper, we consider the Euler method for backward stochastic Volterra integral equations. First, we approximate the original equation by a family of backward stochastic equations (BSDEs, for short). Then we solve the BSDEs by the Euler method. Finally, by virtue of the numerical solutions to BSDEs, we get the numerical solution to original equation and obtain the global $1/2$ order convergence speed in $L^2$ norm.

math.NA↗
arXiv2016

Exact Controllability of Linear Stochastic Differential Equations and Related Problems

A notion of $L^p$-exact controllability is introduced for linear controlled (forward) stochastic differential equations, for which several sufficient conditions are established. Further, it is proved that the $L^p$-exact controllability, the validity of an observability inequality for the adjoint equation, the solvability of an optimization problem, and the solvability of an $L^p$-type norm optimal control problem are all equivalent.

math.OC↗
arXiv2015

A Semidiscrete Galerkin Scheme for Backward Stochastic Parabolic Differential Equations

In this paper, we present a numerical scheme to solve the initial-boundary value problem for backward stochastic partial differential equations of parabolic type. Based on the Galerkin method, we approximate the original equation by a family of backward stochastic differential equations (BSDEs, for short), and then solve these BSDEs by the time discretization. Combining the truncation with respect to the spatial variable and the backward Euler method on time variable, we obtain the global $L^2$ error estimate.

math.OC↗
arXiv2015

Partial regularity of suitable weak solutions to the multi-dimensional generalized magnetohydrodynamics equations

In this paper, we are concerned with the partial regularity of the suitable weak solutions to the fractional MHD equations in $\mathbb{R}^{n}$ for $n=2,\,3$. In comparison with the work of the 3D fractional Navier-Stokes equations obtained by Tang and Yu in [24, Commun. Math. Phys. 334: 1455--1482, 2015], our results include their endpoint case $α=3/4$ and the external force belongs to more general parabolic Morrey space. Moreover, we prove some interior regularity criteria just via the scaled mixed norm of the velocity for the suitable weak solutions to the fractional MHD equations.

math.AP↗
arXiv2014

Anisotropic regularity conditions for the suitable weak solutions to the 3d Navier-Stokes equations

We are concerned with the problem,originated from Seregin [18,19,20], what are minimal sufficiently conditions for the regularity of suitable weak solutions to the 3d Naiver-Stokes equations. We prove some interior regularity criteria, in terms of either one component of the velocity with sufficiently small local scaled norm and the rest part with bounded local scaled norm, or horizontal part of the vorticity with sufficiently small local scaled norm and the vertical part with bounded local scaled norm. It is also shown that only the smallness on the local scaled $L^{2}$ norm of horizontal gradient without any other condition on the vertical gradient can still ensure the regularity of suitable weak solutions. All these conclusions improve pervious results on the local scaled norm type regularity conditions.

math.AP↗
arXiv2014

How are identifiers named in open source software? About popularity and consistency

With the rapid increasing of software project size and maintenance cost, adherence to coding standards especially by managing identifier naming, is attracting a pressing concern from both computer science educators and software managers. Software developers mainly use identifier names to represent the knowledge recorded in source code. However, the popularity and adoption consistency of identifier naming conventions have not been revealed yet in this field. Taking forty-eight popular open source projects written in three top-ranking programming languages Java, C and C++ as examples, an identifier extraction tool based on regular expression matching is developed. In the subsequent investigation, some interesting findings are obtained. For the identifier naming popularity, it is found that Camel and Pascal naming conventions are leading the road while Hungarian notation is vanishing. For the identifier naming consistency, we have found that the projects written in Java have a much better performance than those written in C and C++. Finally, academia and software industry are urged to adopt the most popular naming conventions consistently in their practices so as to lead the identifier naming to a standard, unified and high-quality road.

cs.SE↗