# American Institute of Mathematical Sciences

March  2015, 8(1): 53-77. doi: 10.3934/krm.2015.8.53

## On the Boltzmann equation with the symmetric stable Lévy process

 1 Department of Mathematics, College of Natural Sciences, Chung-Ang University, 84 Heukseok-Ro, Dongjak-Gu, Seoul 156-756

Received  June 2014 Revised  October 2014 Published  December 2014

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 Lévy 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.
Citation: Yong-Kum Cho. On the Boltzmann equation with the symmetric stable Lévy process. Kinetic & Related Models, 2015, 8 (1) : 53-77. doi: 10.3934/krm.2015.8.53
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