報告人：姬傑 (南京航空航天大學)

報告題目：Existence, uniqueness and smoothing effect for spatially homogeneous Landau-Coulomb equation   in $H^{-\f12}$ space with polynomial tail

報告摘要：We demonstrate that the spatially homogeneous Landau-Coulomb equation exhibits global well-posedness in the space $H^{-\f12,\sss}_3\cap L^1_{7}\cap L\log L$ with $\sss>1/2$. Additionally, we furnish several quantitative assessments regarding the smoothing estimates in weighted Sobolev spaces for various initial data configurations. Consequently,  we confirm the conjecture that the solution possesses a $C^\infty$ smoothing effect for any positive time, similar to the heat equation, despite the initial data having only a polynomial tail.

報告時間：2024年11月27日（星期三）16:30-18:00

報告地點：東32樓115會議室

邀請人：雷遠傑

報告人簡介：姬傑，講師，南京航空航天大學，博士畢業于清華大學。主要從事動理學方程的适定性與穩定性的研究。在 SIAM Journal on Mathematical Analysis等國際期刊上發表論文數篇。