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arXiv · 1510.08611

On the Boltzmann equation with the symmetric stable Levy process

Yong-Kum Cho
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Abstract

As for the spatially homogeneous Boltzmann equation of Maxwellian molecules with the fractional Fokker-Planck diffusion term, we consider the Cauchy problem for its Fourier-transformed version, which can be viewed as a kinetic model for the stochastic time-evolution of characteristic functions associated with the symmetric stable Levy process and the Maxwellian collision dynamics. Under a non-cutoff assumption on the kernel, we establish a global existence theorem with maximum growth estimate, uniqueness and stability of solutions.

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Yong-Kum Cho. 2015-10-29. On the Boltzmann equation with the symmetric stable Levy process. https://arxiv.org/abs/1510.08611

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