### Regularization properties of the 2D homogeneous Boltzmann equation without cutoffRegularization properties of the 2D homogeneous Boltzmann equation without cutoff

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 Author Bally, Vlad ♦ Fournier, Nicolas Source arXiv.org Content type Text File Format PDF Date of Submission 2009-11-13 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics ♦ Physics Subject Keyword Mathematics - Probability ♦ Mathematical Physics ♦ 60H07 ♦ 82C40 ♦ math ♦ physics:math-ph Abstract We consider the 2-dimensional spatially homogeneous Boltzmann equation for hard potentials. We assume that the initial condition is a probability measure that has some exponential moments and is not a Dirac mass. We prove some regularization properties: for a class of very hard potentials, the solution instantaneously belongs to $H^r$, for some $r\in (-1,2)$ depending on the parameters of the equation. Our proof relies on the use of a well-suited Malliavin calculus for jump processes. Educational Use Research Learning Resource Type Article