Year: 2019
CAM-Net Digest, Vol. 16 (2019), Iss. 24 : p. 5
Abstract
举办日期：2019年12月10日 ~ 12月11日
举办地点：武汉大学数学与统计学院
资助单位：国家天元数学中部中心、武汉大学数学与统计学院
课时数：6课时
规模：40人
授课时间：12月10日 15:30-17:30 、12月11日 10:00-12:00 、12月11日 15:30-17:30
课程名称：非截断玻尔兹曼方程的整体适定性 Global well-posedness for the non-cutoff Boltzmann equation
课程简介：The Landau equation with Coulomb potential and the non-cutoff Boltzmann equation for the long range
interaction potentials are two fundamental mathematical models in collisional kinetic theory which describe the dynamics
of a non-equilibrium rarefied gas. These two equations are connected in several ways; for example the Landau equation
can be formally derived from the Boltzmann equation by taking the grazing limit. Further the collision operators in both
equations each feature velocity diffusion which can induce a gain of spatial regularity for spatially inhomogeneous solutions
as a result of the interplay with the free transport operator. The existence theory for both equations has a long history.
A well-established framework in which to study global well-posedness is to look for solutions that are close to the global
Maxwellian equilibria in different function spaces. However, for these two equations it is a big open problem to characterize
the optimal mathematical space of initial data with lower regularity in space and velocity variables such that unique solutions
may exist globally in time. The main goal of this course is to prove the global existence of unique solutions in a new function
space with mild regularity for both equations in the perturbative framework.
导师简介：段仁军，香港中文大学教授。2008 年在香港城市大学获理学博士学位；2008年至2010年在奥地利科学院作博士后研究；曾获钟家庆数学奖等；主持香港研究基金多项；段仁军教授长期从事非线性偏微分方程的研究，特别是在玻尔兹曼方程和耗散性偏微分方程的研究中作出了重要意义的工作，成果发表在在国际上重要杂志如：CPAM，ARMA, CMP, SIAM Math. ANA.上，并在国际上产生了重要的影响。
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Journal Article Details
Publisher Name: Global Science Press
Language: Chinese
DOI: https://doi.org/2019-CAM-13757
CAM-Net Digest, Vol. 16 (2019), Iss. 24 : p. 5
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 1