In this study, we first show a finite time collapse of a three-dimensional Smoluchowski–Poisson system in the micro-canonical ensemble (i.e., μSP system) with positive total energy. Using a precise estimation of the bound of the gravitational contribution to total energy, we provide blow-up conditions on the initial state of the μSP system. The conditions indicate that highly clustered self-gravitating particles in the μSP system induce a finite time collapse, even for positive total energy.
|Number of pages||5|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Publication status||Published - 2018 Oct 1|
Bibliographical noteFunding Information:
This work was supported by the National Research Foundation of Korea (NRF), South Korea grant funded by the Korean government (Ministry of Science and ICT) (No. NRF-20151009350 ).
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Condensed Matter Physics