Abstract
We prove existence, uniqueness and stability for solutions of the nonlinear Boltzmann equation in a periodic box in the case when the initial data are sufficiently close to a spatially homogeneous function. The results are given for a range of spaces, including L 1, and extend previous results in L ∞ for the non-homogeneous equation, as well as the more developed L p-theory for the spatially homogeneous Boltzmann equation.
We also give new L ∞-estimates for the spatially homogeneous equation in the case of Maxwellian interactions.
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Wennberg, B. Stability and exponential convergence for the Boltzmann equation. Arch. Rational Mech. Anal. 130, 103–144 (1995). https://doi.org/10.1007/BF00375152
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DOI: https://doi.org/10.1007/BF00375152