The proposed course discusses the stability of a system consisting of a large number of mutually gravitating particles that do not collide. The beginning of the theory of gravitational stability was laid by the works of Laplace, Maxwell, Kovalevskaya, Lyapunov, Poincare. A system consisting of a large number of particles evolves in accordance with the Vlasov-Poisson equations. This system is analogous to the equations for plasma, and research methods previously developed in plasma physics have led to the study of collective effects in an gravitating medium, beginning with the works of Jeans, Antonov, Linden-Bell, and others.

The work on the stability of the orbits of individual particles was replaced by a statistical description using a density function that satisfies the kinetic equation.

This course is logically related to the course “Paradoxes of thermodynamics and statistical mechanics, stability of the Vlasov kinetic equation solutions”, read in the fall of 2021, but does not require knowledge of the material of the previous course.

Lecturer
Salnikova Tatiana Vladimirovna

Organizations
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center