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June  2015, 8(2): 309-333. doi: 10.3934/krm.2015.8.309

On the homogeneous Boltzmann equation with soft-potential collision kernels

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

Received  August 2014 Revised  January 2015 Published  March 2015

We consider the well-posedness problem for the space-homogeneous Boltzmann equation with soft-potential collision kernels. By revisiting the classical Fourier inequalities and fractional integrals, we deduce a set of bilinear estimates for the collision operator on the space of integrable functions possessing certain degree of smoothness and we apply them to prove the local-in-time existence of a solution to the Boltzmann equation in both integral form and the original one. Uniqueness and stability of solutions are also established.
Citation: Yong-Kum Cho. On the homogeneous Boltzmann equation with soft-potential collision kernels. Kinetic & Related Models, 2015, 8 (2) : 309-333. doi: 10.3934/krm.2015.8.309
References:

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References:
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