One Day Workshop at NCKU DATE 2023-03-08¡@15:10-16:00 PLACE ¼Æ¾Ç¨tÀ] 3F·|Ä³«Ç SPEAKER ¦¿ª÷«° ±Ð±Â¡]°ê¥ß²MµØ¤j¾Ç¼Æ¾Ç¨t¡^ TITLE On the Cauchy Problem for the Cutoff Boltzmann Equation with small Initial Data ABSTRACT Singularity formation and Cauchy Problem for Some Nonlinear PDEs Organizers: ¤è¥Ã´I¡A¥v²ß°¶¡A³¢ÂE¤å¡AÃö¦¼µY Goal: We arrange a series of lectures at introductory level and hope to attract students to appreciate some merits of the PDE topic We prove the global existence of the non-negative unique mild solution for the Cauchy problem of the cutoff Boltzmann equation for soft potential model $-1\leq \gamma< 0$ with the small initial data in three dimensional space. The novel contribution of this work lies in the exploration of the symmetric property of the gain term in terms of weighted estimate. It is the key ingredient for solving the model $-1<\gamma<0$ when applying the Strichartz estimates. This talk is based on the joint work with L.-B. He.