ON THE HOMOGENEOUS BOLTZMANN EQUATION WITH SOFT-POTENTIAL COLLISION KERNELS

초록

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.

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