A Revision on Classical Solutions to the Cauchy Boltzmann Problem for Soft Potentials

作者：Alonso Ricardo J; Gamba Irene M^*

来源：Journal of Statistical Physics, 2011, 143(4): 740-746.

DOI：10.1007/s10955-011-0205-z

• Boltzmann equation for soft potentials
• Generalized and classical solutions
• Stability in L(p) spaces

This short note complements the recent paper of the authors (Alonso, Gamba in J. Stat. Phys. 137(5-6):1147-1165, 2009). We revisit the results on propagation of regularity and stability using L(p) estimates for the gain and loss collision operators which had the exponent range misstated for the loss operator. We show here the correct range of exponents. We require a Lebesgue's exponent alpha > 1 in the angular part of the collision kernel in order to obtain finiteness in some constants involved in the regularity and stability estimates. As a consequence the L(p) regularity associated to the Cauchy problem of the space inhomogeneous Boltzmann equation holds for a finite range of p >= 1 explicitly determined.

• 出版日期2011-5