The Cauchy problem for the radially symmetric homogeneous Boltzmann equation with Shubin class initial datum and Gelfand-Shilov smoothing effect (Q2013925)

This work considers the spatially homogeneous Boltzmann equation with bilinear collision operator, which describes Maxwellian molecules, i.e., the non-negative cross section depends on the collision angle only. Thus, the corresponding Cauchy problem is reformulated in terms of the Cauchy problem for the fluctuation of the density distribution function near the Maxwell distribution for velocities. The principal result is that the Cauchy problem admits a global radially symmetric weak solution in the case, when the initial data belongs to the Shubin space of the negative index, and the Gelfand-Shilov smoothing effect occurs in this case.