講座主題：The Vlasov-Poisson-Boltzmann/Landau system with polynomial perturbation
專(zhuān)家姓名：鄧定群
工作單位：清華大學(xué)
講座時(shí)間：2022年3月24日 15:00-16:30
講座地點(diǎn)：騰訊會(huì)議：569262113
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)容摘要：
In this talk, we consider the Vlasov-Poisson-Boltzmann system without angular cutoff and the Vlasov-Poisson-Landau system with Coulomb potential near a global Maxwellian $\mu$ in torus or union of cubes. We establish the global existence, uniqueness and large time behavior for solutions in a polynomial-weighted Sobolev space $H^2_{x, v}(\langle v \rangle^k)$ for some constant $k>0$.
For the domain union of cubes, We will consider the specular-reflection boundary condition and its high-order compatible specular boundary condition. The proof is based on extra dissipation term generated from improved semigroup method with the help of macroscopic estimates.
主講人介紹：
鄧定群，清華大學(xué)丘成桐數(shù)學(xué)中心和北京雁棲湖應(yīng)用數(shù)學(xué)研究院博士后。他于2021年獲香港城市大學(xué)博士學(xué)位，之后加入雁棲湖應(yīng)用數(shù)學(xué)研究院。他的研究興趣在偏微分方程：主要是流體動(dòng)力學(xué)方程中的Boltzmann方程，主題有帶邊界的存在性問(wèn)題、在局部Maxwellian附近的擾動(dòng)問(wèn)題、光滑性問(wèn)題和譜分析。研究成果發(fā)表在Commun. Math. Phys.、SIAM J. Math. Anal.、J. Differential Equations等國(guó)際知名學(xué)術(shù)雜志上。
