引力质量在引力作用中的角色,如同电荷在电磁作用中的角色,因此有时引力质量又可称为引力荷。如果从引力荷这一角色看待引力质量,引力质量就应该和电荷一样服从于一定的物理原理或规则。本文根据物理定律之间的逻辑关联性简单地探讨了引力质量所可能具有的一些性质,如相对论不变性、量子化、一致性和守恒性等特性以及一些相关问题。The role that gravitational mass plays in gravitational interaction is the same as that of electric charge in electromagnetic interaction, so gravitational mass is sometimes also called gravitational charge. Gravitational mass, like electric charge, might be subject to some physical principles or rules, if it is looked at from the role of gravitational charge. In this paper, according to the logical relationships between the physical laws, a simple discussion is given on some properties in which gravitational mass might possibly behave, such as relativistic invariance, quantization, consistency and conservativeness, along with some interrelated things.
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).
