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.

Influence of Bottom Inclination on the Flow Structure in a Rotating Convective Layer

The formation of convective flows in a rotating cylindrical layer with an inclined bottom and free surface is studied.Convection is driven by localized cooling at the center of the upper free surface and by rim heating at the bottom near the sidewall.The horizontal temperature difference in a rotating layer leads to the formation of a convective flow with a complex structure.The mean meridional circulation,consisting of three cells,provides a strongly non-uniform differential rotation.As a result of the instability of the main cyclonic zonal flow,the train of baroclinic waves appears in the upper layer.The baroclinic waves provide most of the heat transfer in the middle radii and are responsible for strong temperature and velocity fluctuations.It is shown that the inclination of the bottom is a crucial factor for the structure of the convective cells and the dynamics of the baroclinic waves.The increase in the inclination angle leads to a significant increase in the energy of the waves.The obtained results may be important for heat and mass transfer in various geophysical and industrial systems,including transport of various additives and impurities in rotating crucibles,and crystallization processes.

Discussion on the Importance of Legal English under the Background of Globalization of Legal Services

Under the background of the internationalization of legal services,the legal relationship is becoming more and more complex in the private international law area.The demand for international legal services for compound talents with foreign language as the core is expanding,while the number of transnational legal offices is increasing rapidly.It options a higher demand on the English level of talents involved in transnational legal affairs.This paper tends to analyze the importance of legal English from the perspective of globalization.

An assessment of global ocean wave energy resources over the last 45 a

Against the background of the current world facing an energy crisis,and human beings puzzled by the problems of environment and resources,developing clean energy sources becomes the inevitable choice to deal with a climate change and an energy shortage.A global ocean wave energy resource was reanalyzed by using ERA-40 wave reanalysis data 1957–2002 from European Centre for Medium-Range Weather Forecasts（ECMWF）.An effective significant wave height is defined in the development of wave energy resources（short as effective SWH）,and the total potential of wave energy is exploratively calculated.Synthetically considering a wave energy density,a wave energy level probability,the frequency of the effective SWH,the stability and long-term trend of wave energy density,a swell index and a wave energy storage,global ocean wave energy resources were reanalyzed and regionalized,providing reference to the development of wave energy resources such as wave power plant location,seawater desalination,heating,pumping.

Analysis of the Global Swell Distributions Using ECMWF Re-Analyses Wind Wave Data

The existence of three well-defined tongue-shaped zones of swell dominance,termed as 'swell pools',in the Pacific,the Atlantic and the Indian Oceans,was reported by Chen et al.(2002)using satellite data.In this paper,the ECMWF Re-analyses wind wave data,including wind speed,significant wave height,averaged wave period and direction,are applied to verify the existence of these swell pools.The swell indices calculated from wave height,wave age and correlation coefficient are used to identify swell events.The wave age swell index can be more appropriately related to physical processes compared to the other two swell indices.Based on the ECMWF data the swell pools in the Pacific and the Atlantic Oceans are confirmed,but the expected swell pool in the Indian Ocean is not pronounced.The seasonal variations of global and hemispherical swell indices are investigated,and the argument that swells in the pools seemed to originate mostly from the winter hemisphere is supported by the seasonal variation of the averaged wave direction.The northward bending of the swell pools in the Pacific and the Atlantic Oceans in summer is not revealed by the ECMWF data.The swell pool in the Indian Ocean and the summer northward bending of the swell pools in the Pacific and the Atlan-tic Oceans need to be further verified by other datasets.

Approximate Inertial Manifold for a Class of the Kirchhoff Wave Equations with Nonlinear Strongly Damped Terms

This paper is devoted to the long time behavior of the solution to the initial boundary value problems for a class of the Kirchhoff wave equations with nonlinear strongly damped terms: . Firstly, in order to prove the smoothing effect of the solution, we make efficient use of the analytic property of the semigroup generated by the principal operator of the equation in the phase space. Then we obtain the regularity of the global attractor and construct the approximate inertial manifold of the equation. Finally, we prove that arbitrary trajectory of the Kirchhoff wave equations goes into a small neighbourhood of the approximate inertial manifold after large time.

On the Cauchy Problem for a Class of Nonlinear Wave Equations with Damping Term

The paper concerns with the existence, uniqueness and nonexistence of global solution to the Cauchy problem for a class of nonlinear wave equations with damping term. It proves that under suitable assumptions on nonlinear the function and initial data the abovementioned problem admits a unique global solution by Fourier transform method. The sufficient conditions of nonexistence of the global solution to the above-mentioned problem are given by the concavity method.

Global Well-posedness of the Generalized Long-short Wave Equations

在现在的纸，我们调查概括渴望突然波浪方程的 Cauchy 问题的全球解决方案的 well-posedness。适用的 Kato 为抽象伪线性的进化方程和 priori 的方法答案估计，我们得到全球性光滑的答案的存在。

ALMOST CONSERVATION LAWS AND GLOBAL ROUGH SOLUTIONS OF THE DEFOCUSING NONLINEAR WAVE EQUATION ON R^2

In this article, we investigate the initial value problem（IVP） associated with the defocusing nonlinear wave equation on R^2 as follows：{δttu-△u=-u^3 u（0,x）=u0（x）,δtu＊（0,x）=u1（x,）where the initial data （uo,ul）∈H^s-1（R^2）It is shown that the IVP is global well-posedness in H^s（R^2）×H^s-1×H^s-1（R^2）for any 1 〉 s 〉2/5.The proof relies upon the almost conserved quantity in using multilinear correction term. The main difficulty is to control the growth of the variation of the almost conserved quantity. Finally, we utilize linear-nonlinear decomposition benefited from the ideas of Roy [1].

Adjustment time of the first baroclinic Rossby wave in the global oceans

According to the freely linear Rossby wave theory, global 1°×1°climatology of Rossby deformation radius and phase speed are studied under the fiat bottom fluid approximation. Geographical variations in the contours of the phase speed are very similar to those of the Rossby radius of formation, which are mainly affected by stratification, rotation, water depth, topography, etc. The basin-crossing time of the first baroclinic Rossby wave is obtained and analyzed in the global ocean basins. The results are useful to learn the importance of Rosaby wave and the adiabatic adjustment of large-scale ocean circulation.

Regularity of Global Attractors for the Kirchhoff Wave Equation

In this paper, we mainly use operator decomposition technique to prove the global attractors which in ?for the Kirchhoff wave equation with strong damping and critical nonlinearities, are also bounded in .

SIMILARITY TRANSFORMATION, THE STRUCTURE OF THE TRAVELING WAVES SOLUTION AND THE EXISTENCE OF A GLOBAL SMOOTH SOLUTION TO GENERALIZED KURAMOTO SIVASHINSKY TYPE EQUATIONS

The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.

The Impact of Global Warming on the Pacific Decadal Oscillation and the Possible Mechanism

The response of the Pacific Decadal Oscillation （PDO） to global warming according to the Fast Ocean Atmosphere Model （FOAM） and global warming comparison experiments of 11 IPCC AR4 models is investigated. The results show that North Pacific ocean decadal variability, its dominant mode （i.e., PDO）, and atmospheric decadal variability, have become weaker under global warming, but with PDO shifting to a higher frequency. The SST decadal variability reduction maximum is shown to be in the subpolar North Pacific Ocean and western North Pacific （PDO center）. The atmospheric decadal variability reduction maximum is over the PDO center. It was also found that oceanic baroclinic Rossby waves play a key role in PDO dynamics, especially those in the subpolar ocean. As the frequency of ocean buoyancy increases under a warmer climate, oceanic baroclinic Rossby waves become faster, and the increase in their speed ratio in the high latitudes is much larger than in the low latitudes. The faster baroclinic Rossby waves can cause the PDO to shift to a higher frequency, and North Pacific decadal variability and PDO to become weaker.

LONG-TIME DYNAMICS OF THE STRONGLY DAMPED SEMILINEAR PLATE EQUATION IN R^N

We investigate the initial-value problem for the semilinear plate equation containing localized strong damping, localized weak damping and nonlocal nonlinearity. We prove that if nonnegative damping coefficients are strictly positive almost everywhere in the exterior of some ball and the sum of these coefficients is positive a.e. in R^n, then the semigroup generated by the considered problem possesses a global attractor in H^2（R^n） × L^2（R^n）.We also establish the boundedness of this attractor in H^3（R^n） × H^2（R^n）.

The relationship between the canonical ENSO and the phase transition of the Antarctic oscillation at the quasi-quadrennial timescale

A correlation analysis is performed to investigate the relationship between El Nino-Southern Oscillation （ENSO） and the Antarctic oscillation （AAO） at the quasi-quadrennial （QQ） timescale.It is found that the cold tongue index （CTI） and the AAO index （AAOI） are negatively correlated with about a 7-month lead-time,while they are positively correlated with about a 15-month lag-time.To further explore this relationship,complex empirical orthogonal function analysis is employed in the QQ sea level pressure （SLP） anomalies from 1951 to 2002.The results indicate that,during the ENSO cycle,there exists one kind of global tropical wave of wavenumber 1 （GTW1） propagating eastward.With the traveling of GTW1,the tropical SLP anomaly tends to intrude into the southern mid-latitudes.Accordingly,three strong signals travel synchronously along the circumSouth-Pacific path,and a relatively weak signal extends eastward and poleward over the South Ocean in the Atlantic-Indian Ocean sector.Following the propagation of these signals,the AAO phase tends to be reversed progressively.As a result,there exists an evident lead-lag correlation between CTI and AAOI.It can be concluded that ENSO plays a key role in the phase transition of AAO at the QQ timescale.It is also noticed that this regular relationship is only evident in the canonical ENSO events,for which sea surface temperature （SST） anomalies extend westward from the tropical eastern Pacific.On the other hand,the similar relationships are not found among those atypical ENSO events for which SST anomalies spread eastward from the central Pacific,such as the 1982-1983 ENSO event.

THE GLOBAL AND LOCAL C^(2)-SOLUTIONS FOR THE WAVE EQUATION □u = G(u_t, Du) IN THREE SPACE DIMENSIONS

Kunio Hidano[4] has shown that the global and local C2-solutions for semilinear wave equations with spherical symmetry in three space dimensions. This paper studies the global and local C2-solutions for the semilinear wave equations without spherical symmetry in three space dimensions. A problem put forward by Hiroyuki Takamura[2] is partially answered.

On the Fifth-Order Stokes Solution for Steady Water Waves

This paper presents a universal fifth-order Stokes solution for steady water waves on the basis of potential theory. It uses a global perturbation parameter, considers a depth uniform current, and thus admits the flexibilities on the definition of the perturbation parameter and on the determination of the wave celerity. The universal solution can be extended to that of Chappelear （1961）, confirming the correctness for the universal theory. Furthermore, a particular fifth-order solution is obtained where the wave steepness is used as the perturbation parameter. The applicable range of this solution in shallow depth is analyzed. Comparisons with the Fourier approximated results and with the experimental measurements show that the solution is fairly suited to waves with the Ursell number not exceeding 46.7.

The Development of a Nonhydrostatic Global Spectral Model

With the development of numerical weather prediction technology, the traditional global hydrostatic models used in many countries of the world for operational weather forecasting and numerical simulations of general circulation have become more and more unfit for high-impact weather prediction. To address this, it is important to invest in the development of global nonhydrostatic models. Few existing nonhydrostatic global models use consistently the grid finite difference scheme for the primitive equations of dynamical cores, which can subsequently degrade the accuracy of the calculations. A new nonhydrostatic global spectral model, which utilizes the Eulerian spectral method, is developed here from NCAR Community Atmosphere Model 3.0 （CAM3.0）. Using Janjic＇s hydrostatic/nonhydrostatic method, a global nonhydrostatic spectral method for the primitive equations has been formulated and developed. In order to retain the integrity of the nonhydrostatic equations, the atmospheric curvature correction and eccentricity correction are considered. In this paper, the Held-Suarez idealized test and an idealized baroclinic wave test are first carried out, which shows that the nonhydrostatic global spectral model has similar climate states to the results of many other global models for long-term idealized integration, as well as better simulation ability for short-term idealized integration. Then, a real case experiment is conducted using the new dynamical core with the full physical parameterizations of subgrid-scale physical processes. The 10-day numerical integration indicates a decrease in systematic error and a better simulation of zonal wind, temperature, and 500-hPa height.

Initial value problem for a class of fourth-order nonlinear wave equations

In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given.

GLOBAL ATTRACTOR OF A CLASS OF STRONGLY DAMPED NONLINEAR WAVE EQUATIONS

A class of strongly damped nonlinear wave equations are studied by using the technique of the operator decomposition,and the existence of the global compact attractor in space D(A)×V is obtained.