arXiv subjects
Publications and source records attributed to Anne Niesdroy.
We prove global well-posedness of the hard-sphere Boltzmann equation in $\mathbb{R}^d$ for small initial data in the critical Besov space $B_{1,1}^{d-1}L_v^1$ and in the critical Sobolev space $W^{d-1,1}L_v^1$. The proof is based on new bilinear estimates for the nonlinear collision operator, which rely on transversality considerations.
We show the existence of local and global in time weak martingale solutions for a stochastic version of the Othmer-Dunbar-Alt kinetic model of chemotaxis under suitable assumptions on the turning kernel and stochastic drift coefficients, using dispersion and stochastic Strichartz estimates. The analysis is based on new Strichartz estimates for stochastic kinetic transport. The derivation of these estimates involves a local in time dispersion analysis using properties of stochastic flows, and a time-splitting argument to extend the local in time results to arbitrary time intervals.