In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator esti...In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator estimates are motivated by the study of well-posedness results for some models in incompressible fuid mechanics.展开更多
We study certain weighted Bergman and weighted Besov spaces of holomorphic functions in the polydisk and in the unit ball.We seek conditions on the weight functions to guarantee that the dilations of a given function ...We study certain weighted Bergman and weighted Besov spaces of holomorphic functions in the polydisk and in the unit ball.We seek conditions on the weight functions to guarantee that the dilations of a given function converge to the same function in norm;in particular,we seek conditions on the weights to ensure that the analytic polynomials are dense in the space.展开更多
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
文摘In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator estimates are motivated by the study of well-posedness results for some models in incompressible fuid mechanics.
文摘We study certain weighted Bergman and weighted Besov spaces of holomorphic functions in the polydisk and in the unit ball.We seek conditions on the weight functions to guarantee that the dilations of a given function converge to the same function in norm;in particular,we seek conditions on the weights to ensure that the analytic polynomials are dense in the space.
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 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
