Global Well-Posedness for Aggregation Equation with Time-Space Nonlocal Operator and Shear Flow

In this paper,we consider the two-dimensional aggregation equation with the shear flow and time-space nonlocal attractive operator.Without the advection,the solution of the aggregation equation may blow up in finite time.We show that the shear flow can suppress the blow-up.

DECAY ESTIMATE AND GLOBAL EXISTENCE OF SEMILINEAR THERMOELASTIC TIMOSHENKO SYSTEM WITH TWO DAMPING EFFECTS

In this paper, we study a semilinear Timoshenko system with heat conduction having two damping effects. The observation that two damping effects might lead to smaller decay rates for solutions in comparison to one damping effect is rigorously proved here in providing optimality results. Moreover, the global well-posedness for small data is presented.

Space-time estimates of the 3D bipolar compressible Navier-Stokes-Poisson system with unequal viscosities

The space-time behavior for the Cauchy problem of the 3D compressible bipolar Navier-Stokes-Poisson(BNSP)system with unequal viscosities is given.The space-time estimate of the electric field▽φ=▽(-△)^(-1)(n-Zρ)is the most important in deducing generalized Huygens’principle for the BNSP system and it requires proving that the space-time estimate of n-Zρonly contains the diffusion wave due to the singularity of the operator▽(-△)^(-1).A suitable linear combination of unknowns reformulating the original system into two small subsystems for the special case(with equal viscosities)in Wu and Wang(2017)is crucial for both linear analysis and nonlinear estimates,especially for the space-time estimate of▽φ.However,the benefits from this reformulation will no longer exist in general cases.Here,we study an 8×8 Green’s matrix directly.More importantly,each entry in Green’s matrix contains wave operators in the low-frequency part,which will generally produce Huygens’wave;as a result,one cannot achieve the space-time estimate of n-Zρthat only contains the diffusion wave as before.We overcome this difficulty by taking a more detailed spectral analysis and developing new estimates arising from subtle cancellations in Green’s function.

二维Stokes近似方程组大扰动解的衰减估计

本文结合频谱域划分的方法和能量估计,充分利用方程中的耗散机制,得到二维Stokes近似方程组Cauchy问题大扰动解的一致估计;并在此基础上应用频谱域的划分方法得到解在某个长时间处的小性结合精细的Green函数的方法,本文得到在时间充分大时解的衰减率的估计.本文试图探索在大扰动情形下利用精细的Green函数技术得到解的衰减估计的一般办法.

The Pointwise Estimates of Solutions to the Cauchy Problem of a Chemotaxis Model

This paper deals with an attraction-repulsion chemotaxis model(ARC) in multi-dimensions. By Duhamel's principle, the implicit expression of the solution to(ARC)is given. With the method of Green's function, the authors obtain the pointwise estimates of solutions to the Cauchy problem(ARC) for small initial data, which yield the W s,p(1 ≤p≤∞) decay properties of solutions.

A novel low-cost and environment-friendly cathode with large channels and high structure stability for potassium-ion storage

Potassium-ion batteries (KIBs) are promising candidates for large-scale energy storage due to the abundance of potassium and its chemical similarity to lithium.Nevertheless,the performances of KIBs are still unsatisfactory for practical applications,mainly hindered by the lack of suitable cathode materials.Herein,combining the strong inductive effect of sulphate and the feasible preparation of Fe^(2+)-containing compounds in oxalate system,a compound with novel architecture,K_(4)Fe_(3)(C_(2)O_(4))_(3)(SO_(4))_(2),has been identified as a lowcost and environmentally friendly cathode for stable potassium-ion storage.Its unique crystal structure possesses an unprecedented two-dimensional framework of triple layers,with 3.379Åinterlayer distance and large intralayer rings in the size of 4.576×6.846Å.According to first-principles simulations,such a configuration is favorable for reversible K-ion migration with a very low volume change of 6.4%.Synchrotron X-ray absorption spectra and X-ray diffraction characterizations at different charging/discharging states and electrochemical performances based on its half and full cells further verify its excellent reversibility and structural stability.Although its performance needs to be improved via further composition tuning with multi-valent transition metals,doping,structural optimization,etc.,this study clearly presents a stable structural model for K-ion cathodes with merits of low cost and environmental friendliness.

Design of active and stable catalysts by embedding nitrogen-doped carbon oxygen reduction reaction CoxOy nanoparticles into

The oxygen reduction reaction （ORR） is essential in research pertaining to life science and energy. In applications, platinum-based catalysts give ideal reactivity, but, in practice, are often subject to high costs and poor stability. Some costefficient transition metal oxides have exhibited excellent ORR reactivity, but the stability and durability of such alternative catalyst materials pose serious challenges. Here, we present a facile method to fabricate uniform CoxOy nanoparticles and embed them into N-doped carbon, which results in a composite of extraordinary stability and durability, while maintaining its high reactivity. The half-wave potential shows a negative shift of only 21 mV after 10,000 cycles, only one third of that observed for Pt/C （63 mV）. Furthermore, after 100,000 s testing at a constant potential, the current decreases by only 17%, significantly less than for Pt/C （35%）. The exceptional stability and durability results from the system architecture, which comprises a thin carbon shell that prevents agglomeration of the CoxOy nanoparticles and their detaching from the substrate.

Large-Time Behavior of Periodic Solutions to Fractal Burgers Equation with Large Initial Data

The asymptotic behavior of periodic solutions to fractal nonlinear Burgers equation is considered and the initial data are allowed to be arbitrarily large.The exponential decay estimates of the solutions are obtained for the power of Laplacian α∈[1/2,1).

Global regularity for 3D magneto-hydrodynamics equations with only horizontal dissipation

We investigate the Cauchy problem for the 3D magneto-hydrodynamics equations with only horizontal dissipation for the small initial data. With the help of the dissipation in the horizontal direction and the structure of the system, we analyze the properties of the decay of the solution and apply these decay properties to get the global regularity of the solution. In the process, we mainly use the frequency decomposition in Green's function method and energy method.

Green函数与非线性发展方程解的大时间状态

本文讨论用Green函数方法研究非线性发展方程初值问题解的大时间状态的逐点估计.在简要介绍Green函数的基本思想后,本文通过两个例子说明,对带耗散和双曲结构的非线性发展方程,其相应初值问题的解在双曲机制、抛物机制和非线性机制作用下,如何通过Green函数的方法厘清各种机制的作用,清晰看到其精细结构,并解释其他方法难以解释的一些令人诧异的现象.

带非局部耗散项的守恒律方程大扰动解的整体存在性

本文考虑带非局部耗散项的单个守恒律方程大扰动解的整体存在性.首先,针对方程次临界和临界两种不同的情形,利用Green函数方法和环形分解的技巧,构造开放式高频估计方法,得到了一个新的解的正则性准则.然后,利用极大值原理得到方程解的极大模的有界性,验证了次临界情形下解满足相应的正则性准则.对于临界这一更困难的情形,本文应用非线性极大值原理方法得到了更好一点的有界性估计,验证了临界情形下解也满足相应的正则性准则,从而得到了Cauchy问题大扰动经典解的整体存在性.

混合机制对半线性热方程解爆破的抑制作用

本文考虑带有混合机制的半线性热方程,混合机制是通过加入含不可压流的对流项实现的.在没有混合机制时,方程的解在有限时间会发生爆破.在对流项合适的混合条件下,本文研究方程的大初值整体解的适定性.对于带有混合机制的经典半线性热方程,本文通过能量方法得到了整体的Lp(p>d/2)估计,并且获得了经典解的整体存在性.然而,对于带有混合机制的分数阶半线性热方程,由于技术困难,通过能量方法无法得到整体的Lp (p> 2)估计,这里利用非线性极值原理得到了整体的L∞估计,并且获得了经典解的整体存在性.