It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to ...It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w).展开更多
The initial\|irregular oblique derivative boundary value problems for linear and nondivergence parabolic complex equations of second order in multiply connected domains are dealt with, where the coefficients of equati...The initial\|irregular oblique derivative boundary value problems for linear and nondivergence parabolic complex equations of second order in multiply connected domains are dealt with, where the coefficients of equations are measurable. Firstly the uniqueness of solutions for the above problems is introduced, and then some \%a priori\% estimates of solutions for the problems are given. By using the above estimates and the Leray\|Schauder theorem, the existence of solutions of the initial\|boundary value problems can be proved. The results are generalizations of corresponding theorems in literature.展开更多
We present a new method for the existence and pointwise estimates of a Green's function of non-divergence form elliptic operator with Dini mean oscillation coefficients.We also present a sharp comparison with the ...We present a new method for the existence and pointwise estimates of a Green's function of non-divergence form elliptic operator with Dini mean oscillation coefficients.We also present a sharp comparison with the corresponding Green5s function for constant coefficients equations.展开更多
From Maxwell’ s equations for electromagnetic fields, time-averaged energy flow density vector of stable monochromatic linearly polarized light in an isotropic insulative nonmagnetic medium is deduced. By the introdu...From Maxwell’ s equations for electromagnetic fields, time-averaged energy flow density vector of stable monochromatic linearly polarized light in an isotropic insulative nonmagnetic medium is deduced. By the introduction of time-averaged energy flow density rays and the definition of new generalized refractive indexn G1, Fermat’s principle of geometric optics is further generalized and its application conditions are discussed. The generalized Fermat' s principle can be used to describe stable transmission of light in a medium with variable refractive index. The necessary and sufficient conditions of a nondivergent and nonfocusing light beam are derived from this Fermat’s principle.展开更多
Introducing the concept of pseudo-momentum, a generalized Arnold-Dikii functional is established, and then the sufficient condition for stability of nonlinear wave motion in the barotropic nondivergent atmosphere is d...Introducing the concept of pseudo-momentum, a generalized Arnold-Dikii functional is established, and then the sufficient condition for stability of nonlinear wave motion in the barotropic nondivergent atmosphere is derived by use of variational principle. It is found that the stability of nonlinear wave motion depends not only on its streamfield distri- bution, but also on its phase speed for the propagating nonlinear wave motion. Moreover, the stability criterion of trav- elling modon is also obtained, and it is shown that the travelling modon is stable if the scale of disturbance superimposed on the travelling modon remains to be less than that of the travelling modon.展开更多
Variable coefficient nonlinear systems, the Korteweg de Vries （KdV）, the modified KdV （mKdV） and the nonlinear Schrǒdinger （NLS） type equations, are derived from the nonlinear inviscid barotropic nondivergent v...Variable coefficient nonlinear systems, the Korteweg de Vries （KdV）, the modified KdV （mKdV） and the nonlinear Schrǒdinger （NLS） type equations, are derived from the nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane by means of the multi-scale expansion method in two different ways, with and without the so-called y-average trick. The non-auto-Bǎcklund transformations are found to transform the derived variable coefficient equations to the corresponding standard KdV, mKdV and NLS equations. Thus, many possible exact solutions can be obtained by taking advantage of the known solutions of these standard equations. Further, many approximate solutions of the original model are ready to be yielded which might be applied to explain some real atmospheric phenomena, such as atmospheric blocking episodes.展开更多
2006年7月19—24日,东北地区出现一次明显的冷涡发展导致强降水的过程.对这次东北冷涡过程的天气形势分析表明,该东北冷涡的维持和发展与冷涡东部阻塞高压的建立与消亡有关.本文根据500hPa环流形势演变特征,将东北冷涡发生发展过程分为...2006年7月19—24日,东北地区出现一次明显的冷涡发展导致强降水的过程.对这次东北冷涡过程的天气形势分析表明,该东北冷涡的维持和发展与冷涡东部阻塞高压的建立与消亡有关.本文根据500hPa环流形势演变特征,将东北冷涡发生发展过程分为4个阶段,并借助调和-余弦谱展开方法,对东北冷涡各阶段850hPa水平风和水汽通量进行无辐散和无旋转分量分解,分析各阶段无旋转风动能和无辐散风动能之间的能量转化.研究结果表明,分解得到的无辐散风及其水汽通量清楚地展现出了东北冷涡的大尺度环流和水汽输送通道及水汽来源,而从无旋转风及其水汽通量上则可以直观地看到冷涡低层的中小尺度风场及水汽辐合辐散区,为分析东北冷涡内部对流提供帮助.东北冷涡发展的不同阶段其水汽来源有所不同,初始阶段的水汽主要来自黄海和渤海地区,发展阶段水汽主要来自日本海,而到成熟阶段和减弱阶段,水汽输送通道被破坏,冷涡的水汽供应大大减少,与同时期暴雨减弱一致.同时,无旋转风辐合强值区和无旋转风水汽通量大值区的重合区域有利于强对流的发生发展,表现为重合区与TBB(Temperature of Black Body,黑体辐射温度)强对流云带的形状和位置对应良好,与降水落区也较为一致,可为预报东北冷涡引发的强降水落区这一预报难点问题提供参考.从动能转化上看,无旋转风和无辐散风的动能转化项能很好地反映东北冷涡整个生命史过程中各阶段强度的变化特点,对冷涡强度预报具有一定的指示意义.展开更多
文摘It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w).
文摘The initial\|irregular oblique derivative boundary value problems for linear and nondivergence parabolic complex equations of second order in multiply connected domains are dealt with, where the coefficients of equations are measurable. Firstly the uniqueness of solutions for the above problems is introduced, and then some \%a priori\% estimates of solutions for the problems are given. By using the above estimates and the Leray\|Schauder theorem, the existence of solutions of the initial\|boundary value problems can be proved. The results are generalizations of corresponding theorems in literature.
基金partially supported by National Research Foundation of Korea(NRF)Grant No.NRF-2019R1A2C2002724 and No.NRF-20151009350.
文摘We present a new method for the existence and pointwise estimates of a Green's function of non-divergence form elliptic operator with Dini mean oscillation coefficients.We also present a sharp comparison with the corresponding Green5s function for constant coefficients equations.
基金Supported by National Natural Science Foundation of China(11001221)Mathematical Tianyuan Foundation of China(11126027)Northwestern Polytechnical University Jichu Yanjiu Jijin Tansuo Xiangmu(JC201124)
基金Project supported by the National Natural Science Foundation of China (Grant No. 69789801)Guangdong Provincial Natural Science Foundation of China.
文摘From Maxwell’ s equations for electromagnetic fields, time-averaged energy flow density vector of stable monochromatic linearly polarized light in an isotropic insulative nonmagnetic medium is deduced. By the introduction of time-averaged energy flow density rays and the definition of new generalized refractive indexn G1, Fermat’s principle of geometric optics is further generalized and its application conditions are discussed. The generalized Fermat' s principle can be used to describe stable transmission of light in a medium with variable refractive index. The necessary and sufficient conditions of a nondivergent and nonfocusing light beam are derived from this Fermat’s principle.
文摘Introducing the concept of pseudo-momentum, a generalized Arnold-Dikii functional is established, and then the sufficient condition for stability of nonlinear wave motion in the barotropic nondivergent atmosphere is derived by use of variational principle. It is found that the stability of nonlinear wave motion depends not only on its streamfield distri- bution, but also on its phase speed for the propagating nonlinear wave motion. Moreover, the stability criterion of trav- elling modon is also obtained, and it is shown that the travelling modon is stable if the scale of disturbance superimposed on the travelling modon remains to be less than that of the travelling modon.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10735030, 10547124, 90503006 and 40305009)the National Basic Research Program of China (Grant Nos 2007CB814800 and 2005CB422301)+3 种基金Specialized Research Fund for the Doctoral Program of Higher Education (Grant No 20070248120)Program for Changjiang Scholars and Innovative Research Team in University (Grant No IRT0734)the Scientific Research Starting Foundation for Returned Overseas Chinese Scholars, Ministry of Education, Chinathe Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No NCET-05-0591)
文摘Variable coefficient nonlinear systems, the Korteweg de Vries （KdV）, the modified KdV （mKdV） and the nonlinear Schrǒdinger （NLS） type equations, are derived from the nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane by means of the multi-scale expansion method in two different ways, with and without the so-called y-average trick. The non-auto-Bǎcklund transformations are found to transform the derived variable coefficient equations to the corresponding standard KdV, mKdV and NLS equations. Thus, many possible exact solutions can be obtained by taking advantage of the known solutions of these standard equations. Further, many approximate solutions of the original model are ready to be yielded which might be applied to explain some real atmospheric phenomena, such as atmospheric blocking episodes.
文摘2006年7月19—24日,东北地区出现一次明显的冷涡发展导致强降水的过程.对这次东北冷涡过程的天气形势分析表明,该东北冷涡的维持和发展与冷涡东部阻塞高压的建立与消亡有关.本文根据500hPa环流形势演变特征,将东北冷涡发生发展过程分为4个阶段,并借助调和-余弦谱展开方法,对东北冷涡各阶段850hPa水平风和水汽通量进行无辐散和无旋转分量分解,分析各阶段无旋转风动能和无辐散风动能之间的能量转化.研究结果表明,分解得到的无辐散风及其水汽通量清楚地展现出了东北冷涡的大尺度环流和水汽输送通道及水汽来源,而从无旋转风及其水汽通量上则可以直观地看到冷涡低层的中小尺度风场及水汽辐合辐散区,为分析东北冷涡内部对流提供帮助.东北冷涡发展的不同阶段其水汽来源有所不同,初始阶段的水汽主要来自黄海和渤海地区,发展阶段水汽主要来自日本海,而到成熟阶段和减弱阶段,水汽输送通道被破坏,冷涡的水汽供应大大减少,与同时期暴雨减弱一致.同时,无旋转风辐合强值区和无旋转风水汽通量大值区的重合区域有利于强对流的发生发展,表现为重合区与TBB(Temperature of Black Body,黑体辐射温度)强对流云带的形状和位置对应良好,与降水落区也较为一致,可为预报东北冷涡引发的强降水落区这一预报难点问题提供参考.从动能转化上看,无旋转风和无辐散风的动能转化项能很好地反映东北冷涡整个生命史过程中各阶段强度的变化特点,对冷涡强度预报具有一定的指示意义.
