Mathematical Analysis of Dilute Classical Gases

• Applicant: Dr. Sergio Simonella
• Subject Area: Mathematics
• Term: from 2015 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 269134396

We study the theory of dynamical fluctuations around the Boltzmann equation. We investigate the short time validity of a central limit theorem in the Boltzmann-Grad limit of a hard sphere system. We expect to prove that the fluctuation field converges to a Gaussian random field governed by a (stochastic) fluctuating Boltzmann equation. This would complement the result of Lanford on the mathematical validity of the theory of Boltzmann. The programme includes an analysis of static (fixed time) fluctuations in the low-density gas, propagation in time of phase space correlations, and space time correlations.Our setting is the general, out of equilibrium, inhomogeneous system. In the particular case of fluctuations around equilibrium, we attempt to extend the results to long times. In parallel, we investigate analytically and numerically the correlations and the statistics of collisions in a low-density gasSome additional problems concerning derivation from particle systems and irreversibility issues are approached.

• DFG Programme: Research Grants