本文研究了Benjamin-Bona-Mahony (BBM)方程在非齐次Besov空间B2,rs(ℝ)中的全局适定性。首先用了压缩映射原理证明了当1≤p≤∞,1r≤∞及s>1p(或1≤p≤∞,r=1及s≥1p)时,BBM方程在Bp,rs(ℝ)中局部适定的。接着,用高低频分解技巧及算...本文研究了Benjamin-Bona-Mahony (BBM)方程在非齐次Besov空间B2,rs(ℝ)中的全局适定性。首先用了压缩映射原理证明了当1≤p≤∞,1r≤∞及s>1p(或1≤p≤∞,r=1及s≥1p)时,BBM方程在Bp,rs(ℝ)中局部适定的。接着,用高低频分解技巧及算子半群理论证明了当1/2s≤1,2≤r∞时,BBM方程在B2,rs(ℝ)中全局适定。In this study, we devoted to the global well-posedness for the Benjamin-Bona-Mahony (BBM) equation in the Nonhomogeneous Besov spaces B2,rs(ℝ)First, using the contraction mapping principle, it is proved that when 1≤p≤∞,1r≤∞and s>1p(or 1≤p≤∞, r=1and s≥1p), the BBM is locally well-posed in Bp,rs(ℝ)(or in Bp,1s(ℝ)). Then using Bourgain’s low-high frequency decomposition technique, it is proved that when 12s≤1and 2≤r∞, BBM is globally well-posed in Besov spaces B2,rs(ℝ).展开更多
The special structure in some coupled equations makes it possible to drop partial smallness assumption of the initial data to gain the global well-posedness.In this paper,we study the Cauchy problem for generalized De...The special structure in some coupled equations makes it possible to drop partial smallness assumption of the initial data to gain the global well-posedness.In this paper,we study the Cauchy problem for generalized Debye-Hückel system in Fourier-Besov spaces.Under more generalized index range,we obtain the global solution with small initial data and local solution with arbitrary initial.Besides,by constructing some weighted function,we prove that the global well-posedness still holds under the small assumption of the charge of initial data.Thus we show that although the initial densities and the hole in electrolytes are large,the equation is still global well-posedness.展开更多
In this article, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderón-Zygmund type estimate in Be...In this article, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderón-Zygmund type estimate in Besov spaces with more general assumptions on coefficients for both homogeneous equations and non-homogeneous equations. This study of regularity estimates expands the Calderón-Zygmund theory in the Heisenberg group.展开更多
本文得到了调和Besov空间中函数的泰勒系数增长性的一个估计,也证明了调和Besov空间中的函数关于Bergman度量是Lipschitz连续的。In this paper, we obtain an estimate of the growth of the Taylor coefficient of functions in harmo...本文得到了调和Besov空间中函数的泰勒系数增长性的一个估计,也证明了调和Besov空间中的函数关于Bergman度量是Lipschitz连续的。In this paper, we obtain an estimate of the growth of the Taylor coefficient of functions in harmonic Besov spaces and prove that functions in harmonic Besov spaces are Lipschitz continuous with respect to the Bergman metric.展开更多
文摘本文研究了Benjamin-Bona-Mahony (BBM)方程在非齐次Besov空间B2,rs(ℝ)中的全局适定性。首先用了压缩映射原理证明了当1≤p≤∞,1r≤∞及s>1p(或1≤p≤∞,r=1及s≥1p)时,BBM方程在Bp,rs(ℝ)中局部适定的。接着,用高低频分解技巧及算子半群理论证明了当1/2s≤1,2≤r∞时,BBM方程在B2,rs(ℝ)中全局适定。In this study, we devoted to the global well-posedness for the Benjamin-Bona-Mahony (BBM) equation in the Nonhomogeneous Besov spaces B2,rs(ℝ)First, using the contraction mapping principle, it is proved that when 1≤p≤∞,1r≤∞and s>1p(or 1≤p≤∞, r=1and s≥1p), the BBM is locally well-posed in Bp,rs(ℝ)(or in Bp,1s(ℝ)). Then using Bourgain’s low-high frequency decomposition technique, it is proved that when 12s≤1and 2≤r∞, BBM is globally well-posed in Besov spaces B2,rs(ℝ).
基金Supported by Natural Science Foundation of Jiangsu Province(No.BK20200587)。
文摘The special structure in some coupled equations makes it possible to drop partial smallness assumption of the initial data to gain the global well-posedness.In this paper,we study the Cauchy problem for generalized Debye-Hückel system in Fourier-Besov spaces.Under more generalized index range,we obtain the global solution with small initial data and local solution with arbitrary initial.Besides,by constructing some weighted function,we prove that the global well-posedness still holds under the small assumption of the charge of initial data.Thus we show that although the initial densities and the hole in electrolytes are large,the equation is still global well-posedness.
文摘In this article, we deal with weak solutions to non-degenerate sub-elliptic equations in the Heisenberg group, and study the regularities of solutions. We establish horizontal Calderón-Zygmund type estimate in Besov spaces with more general assumptions on coefficients for both homogeneous equations and non-homogeneous equations. This study of regularity estimates expands the Calderón-Zygmund theory in the Heisenberg group.
文摘本文得到了调和Besov空间中函数的泰勒系数增长性的一个估计,也证明了调和Besov空间中的函数关于Bergman度量是Lipschitz连续的。In this paper, we obtain an estimate of the growth of the Taylor coefficient of functions in harmonic Besov spaces and prove that functions in harmonic Besov spaces are Lipschitz continuous with respect to the Bergman metric.
基金Supported by National Natural Sciences Foundation (10 14 10 0 1) Zhejiang NaturalSciences Foundation (10 2 0 6 6 ) and the Doctorate Fundation (0 2 J2 0 10 2 - 0 6 ) of Ningbo City
