GLOBAL SOLUTIONS TO 1D COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM WITH DENSITY-DEPENDENT VISCOSITY AND FREE-BOUNDARY

This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(ρ)=ρ^(α).The existence of unique global H^(2m)-solutions(m∈N)to the free boundary problem is proven for when 0<α<1/4.Furthermore,we obtain the global C^(∞)-solutions if the initial data is smooth.

GLOBAL CLASSICAL SOLUTIONS OF SEMILINEAR WAVE EQUATIONS ON R^(3)×T WITH CUBIC NONLINEARITIES

In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the cubic form.The main ingredient here is the establishment of the L^(2)-L^(∞)decay estimates and the energy estimates for the linear problem,which are adapted to the wave equation on the product space.The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction,the scaling technique,and the combination of the decay estimates and the energy estimates.

GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH p-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE

This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.

THE GLOBAL EXISTENCE OF STRONG SOLUTIONS TO THERMOMECHANICAL CUCKER-SMALE-STOKES EQUATIONS IN THE WHOLE DOMAIN

We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.

Irrigating Shared Prosperity The World Water Forum convened to explore solutions for the future of global water governance

Consensus was reached by delegates to the 10th World Water Forum that global water-related challenges remain acute,water resources are under serious threat,and wisdom,contributions,and cooperation from around the world are urgently required for water security and shared prosperity.

THE GLOBAL EXISTENCE AND ANALYTICITY OF A MILD SOLUTION TO THE 3D REGULARIZED MHD EQUATIONS

In this paper,we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms.We establish the global existence of mild solutions to this system with small initial data.In addition,we also obtain the Gevrey class regularity and the temporal decay rate of the solution.

BRI:A Chinese Solution to Global Development

Path of Hope:The Global Impact of the Belt and Road Initiative Compiled by the 21st Century Business Herald’s Department of Overseas News Paperback,308 pages Price:RMB 88 Published by Foreign Languages Press Path of Hope:The Global Impact of the Belt and Road Initiative is written by senior international journalists at the Department of Overseas News of the 21st Century Business Herald,a leading business newspaper in China.

Global Existence of the Solution for a Reduced Model of the Vectorial Quantum Zakharov System

In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the global existence of the solution to this system without any small condition on the initial data.

Global Existence and Decay of Solutions for a Class of a Pseudo-Parabolic Equation with Singular Potential and Logarithmic Nonlocal Source

This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.

Oruxmaps软件结合Global Mapper软件在矿产资源行业并购中的应用

纸质地质图结合手持GPS,采用手工方式野外记录的传统地质调查工作方式已不能适应数字化和信息化的要求,在矿产资源并购项目中,运用Oruxmaps、Global Mapper等软件,可以制作适应地质调查工作所特需的离线地质图,实现地质图、GPS定位、路线轨迹记录、文字记录、影像记录等的有机结合,形成了一套行之有效的工作流程,极大地提高了路线地质调查工作的质量和效率。

GLOBAL CLASSICAL SOLUTIONS AND THE CLASSICAL LIMIT OF THE NON-RELATIVISTIC VLASOV-DARWIN SYSTEM WITH SMALL INITIAL DATA

We investigate the global classical solutions of the non-relativistic Vlasov-D arwin system with generalized variables(VDG)in three dimensions.We first prove the global existence and uniqueness for small initial data and derive the decay estimates of the Darwin potentials.Then,we show in this framework that the solutions converge in a pointwise sense to solutions of the classical Vlasov-Poisson system(VP)at the asymptotic rate of 1/c2 as the speed of light c tends to infinity for all time.Moreover,we obtain rigorously an asymptotic estimate of the difference between the two systems.

GLOBAL SOLUTIONS TO A HYDRODYNAMIC MODEL FOR SEMICONDUCTORS WITH VELOCITY RELAXATION

In this paper,we apply the method given in the paper“Zero relaxation time limits to a hydrodynamic model of two carrier types for semiconductors”(Mathematische Annalen,2022,382:1031–1046)to study the Cauchy problem for a one dimensional inhomogeneous hydrodynamic model of two-carrier types for semiconductors with the velocity relaxation.

GLOBAL SOLUTIONS TO THE 2D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH SOME LARGE INITIAL DATA

We consider the global well-posedness of strong solutions to the Cauchy problem of compressible barotropic Navier-Stokes equations in R^(2). By exploiting the global-in-time estimate to the two-dimensional(2D for short) classical incompressible Navier-Stokes equations and using techniques developed in(SIAM J Math Anal, 2020, 52(2): 1806–1843), we derive the global existence of solutions provided that the initial data satisfies some smallness condition. In particular, the initial velocity with some arbitrary Besov norm of potential part Pu_0 and large high oscillation are allowed in our results. Moreover, we also construct an example with the initial data involving such a smallness condition, but with a norm that is arbitrarily large.

Global Existence of Smooth Solutions for the One-Dimensional Full Euler System for a Dusty Gas

We study the existence of global-in-time classical solutions for the one-dimensional nonisentropic compressible Euler system for a dusty gas with large initial data.Using the characteristic decomposition method proposed by Li et al.(Commun Math Phys 267:1–12,2006),we derive a group of characteristic decompositions for the system.Using these characteristic decompositions,we find a sufficient condition on the initial data to ensure the existence of global-in-time classical solutions.

GLOBAL WEAK SOLUTIONS OF COMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ-MAXWELL EQUATIONS FOR QUANTUM FLUIDS IN DIMENSION THREE

In this paper,we consider the weak solutions of compressible Navier-StokesLandau-Lifshitz-Maxwell(CNSLLM)system for quantum fluids with a linear density dependent viscosity in a 3D torus.By introducing the cold pressure Pc,we prove the global existence of weak solutions with the pressure P+Pc,where P=Aργwithγ≥1.Our main result extends the one in[13]on the quantum Navier-Stokes equations to the CNSLLM system.

El Niño and the AMO Sparked the Astonishingly Large Margin of Warming in the Global Mean Surface Temperature in 2023

In 2023,the majority of the Earth witnessed its warmest boreal summer and autumn since 1850.Whether 2023 will indeed turn out to be the warmest year on record and what caused the astonishingly large margin of warming has become one of the hottest topics in the scientific community and is closely connected to the future development of human society.We analyzed the monthly varying global mean surface temperature(GMST)in 2023 and found that the globe,the land,and the oceans in 2023 all exhibit extraordinary warming,which is distinct from any previous year in recorded history.Based on the GMST statistical ensemble prediction model developed at the Institute of Atmospheric Physics,the GMST in 2023 is predicted to be 1.41℃±0.07℃,which will certainly surpass that in 2016 as the warmest year since 1850,and is approaching the 1.5℃ global warming threshold.Compared to 2022,the GMST in 2023 will increase by 0.24℃,with 88%of the increment contributed by the annual variability as mostly affected by El Niño.Moreover,the multidecadal variability related to the Atlantic Multidecadal Oscillation(AMO)in 2023 also provided an important warming background for sparking the GMST rise.As a result,the GMST in 2023 is projected to be 1.15℃±0.07℃,with only a 0.02℃ increment,if the effects of natural variability—including El Niño and the AMO—are eliminated and only the global warming trend is considered.

Global hybrid simulations of soft X-ray emissions in the Earth’s magnetosheath

Earth’s magnetopause is a thin boundary separating the shocked solar wind plasma from the magnetospheric plasmas,and it is also the boundary of the solar wind energy transport to the magnetosphere.Soft X-ray imaging allows investigation of the large-scale magnetopause by providing a two-dimensional(2-D)global view from a satellite.By performing 3-D global hybrid-particle-in-cell(hybrid-PIC)simulations,we obtain soft X-ray images of Earth’s magnetopause under different solar wind conditions,such as different plasma densities and directions of the southward interplanetary magnetic field.In all cases,magnetic reconnection occurs at low latitude magnetopause.The soft X-ray images observed by a hypothetical satellite are shown,with all of the following identified:the boundary of the magnetopause,the cusps,and the magnetosheath.Local X-ray emissivity in the magnetosheath is characterized by large amplitude fluctuations(up to 160%);however,the maximum line-of-sight-integrated X-ray intensity matches the tangent directions of the magnetopause well,indicating that these fluctuations have limited impact on identifying the magnetopause boundary in the X-ray images.Moreover,the magnetopause boundary can be identified using multiple viewing geometries.We also find that solar wind conditions have little effect on the magnetopause identification.The Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)mission will provide X-ray images of the magnetopause for the first time,and our global hybrid-PIC simulation results can help better understand the 2-D X-ray images of the magnetopause from a 3-D perspective,with particle kinetic effects considered.

Background removal from global auroral images:Data-driven dayglow modeling

Global images of auroras obtained by cameras on spacecraft are a key tool for studying the near-Earth environment.However,the cameras are sensitive not only to auroral emissions produced by precipitating particles,but also to dayglow emissions produced by photoelectrons induced by sunlight.Nightglow emissions and scattered sunlight can contribute to the background signal.To fully utilize such images in space science,background contamination must be removed to isolate the auroral signal.Here we outline a data-driven approach to modeling the background intensity in multiple images by formulating linear inverse problems based on B-splines and spherical harmonics.The approach is robust,flexible,and iteratively deselects outliers,such as auroral emissions.The final model is smooth across the terminator and accounts for slow temporal variations and large-scale asymmetries in the dayglow.We demonstrate the model by using the three far ultraviolet cameras on the Imager for Magnetopause-to-Aurora Global Exploration(IMAGE)mission.The method can be applied to historical missions and is relevant for upcoming missions,such as the Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)mission.

Record-breaking High-temperature Outlook for 2023: An Assessment Based on the China Global Merged Temperature(CMST) Dataset

According to the latest version(version 2.0) of the China global Merged Surface Temperature(CMST2.0) dataset, the global mean surface temperature(GMST) in the first half of 2023 reached its third warmest value since the period of instrumental observation began, being only slightly lower than the values recorded in 2016 and 2020, and historically record-breaking GMST emerged from May to July 2023. Further analysis also indicates that if the surface temperature in the last five months of 2023 approaches the average level of the past five years, the annual average surface temperature anomaly in 2023 of approximately 1.26°C will break the previous highest surface temperature, which was recorded in 2016of approximately 1.25°C(both values relative to the global pre-industrialization period, i.e., the average value from 1850 to1900). With El Ni?o triggering a record-breaking hottest July, record-breaking average annual temperatures will most likely become a reality in 2023.

THE GLOBAL EXISTENCE OF BV SOLUTIONS OF THE ISENTROPIC p-SYSTEM WITH LARGE INITIAL DATA

In this paper,we study the global existence of BV solutions of the initial value problem for the isentropic p-system,where the state equation of the gas is given by P=Av^(-γ).Forγ>1,the general existence result for large initial data has not been obtained.By using the Glimm scheme,Nishida,Smoller and Diperna successively obtained the global existence results for(γ-1)TV(v_(0)(x),u_(0)(x))being small.In the present paper,by adopting a rescaling technique,we improve these results and obtain the global existence result under the condition that(γ-1)^(γ+1)(TV(v_(0)(x)))~(γ-1)(TV(u_(0)(x)))^(2) is small,which implies that,for fixedγ>1,either TV(v_(0)(x))or TV(u_(0)(x))can be arbitrarily large.