The Fisher information of the space-homogeneous Boltzmann equation is non-increasing along the flow for all physically relevant kernels, yielding global well-posedness for very soft potentials.
On th e monotonicity of the Fisher information for the Boltzmann equation, 2024
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Fisher information for solutions of the Boltzmann equation
The Fisher information of the space-homogeneous Boltzmann equation is non-increasing along the flow for all physically relevant kernels, yielding global well-posedness for very soft potentials.