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arXiv · 2102.00657

On the Quantum Boltzmann Equation near Maxwellian and Vacuum

Zhimeng Ouyang·Lei Wu
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Abstract

We consider the non-relativistic quantum Boltzmann equation for fermions and bosons. Using the nonlinear energy method and mild formulation, we justify the global well-posedness when the density function is near the global Maxwellian and vacuum. This work is a generalization and adaptation of the classical Boltzmann theory. Our main contribution is a detailed analysis of the nonlinear operator $Q$ in the quantum context. This is the first piece of a long-term project on the quantum kinetic equations.

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Zhimeng Ouyang, Lei Wu. 2021-02-01. On the Quantum Boltzmann Equation near Maxwellian and Vacuum. https://arxiv.org/abs/2102.00657

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