Global low-regularity solutions to the non-cuto Boltzmann equation in R3

Speaker: Prof. Renjun Duan

Title: Global low-regularity solutions to the non-cuto Boltzmann equation in R3

Time & Venue: 2022.04.08  15:30--16:30  Tencent Meeting ID：873760281

Abstract: A class of low-regularity solutions via the Wiener algebra for the non-cuto Boltzmann equation on the torus was previously introduced in collaboration with Liu, Sakamoto and Strain. In the talk, I will further report how to extend the result to the case of the whole space. In this case, we develop an $L^1-L^\infty$ interplay technique in the Fourier space to overcome the weaker macroscopic dissipation due to diffusion phenomenon in contrast to the torus case. The key is to employ time-weighted estimates motivated from viscous conservation laws. Joint work with Shota Sakamoto and Yoshihiro Ueda.