arXiv:1603.00540 Abstract | arXiv Analytics

arXiv:1603.00540 [math.AP]Abstract References Reviews Resources

A gradient flow approach to the Boltzmann equation

Published 2016-03-02Version 1

We show that the spatially homogeneous Boltzmann equation (with constant collision kernel) evolves as the gradient flow of the entropy with respect to a suitable geometry on the space of probability measures. This geometry is given by a new notion of distance between probability measures, which takes the collision process into account. As a first application, we obtain a novel time-discrete approximation scheme for the homogeneous Boltzmann equation.

Comments: 30 pages, comments are welcome

Categories: math.AP

Keywords: gradient flow approach, probability measures, novel time-discrete approximation scheme, constant collision kernel, spatially homogeneous boltzmann equation

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