学术活动

偏微分方法研讨会

作者:   来源:  时间:2019-01-14

偏微分方法研讨会

时间: 1月14日(周一)14:30-15:15

题目:Sharp regularizing estimates for the gain term of the Boltzmann collision operator

报告人:江金城(清华大学 新竹)

Abstract : We prove the sharp regularizing estimates for the gain term of the Boltzmann collision operator including hard sphere, hard potential and Maxwell molecule models. Our new estimates characterize both regularization and convolution properties of the gain term and have the following features. The regularizing exponent is sharp both in the $L^2$ based inhomogeneous and homogeneous Sobolev spaces which is exact the exponent of the kinetic part of collision kernel. The functions in these estimates belong to a wider scope of (weighted) Lebesgue spaces than the previous regularizing estimates. Furthermore, for the estimates in homogeneous Sobolev spaces,we only need functions lying in Lebesgue spaces instead of weighted Lebesgue spaces, i.e., no loss of weight occurs in this case.

 

时间: 1月14日(周一)15:15-16:00

题目:Wave phenomena to 3D Navier-Stokes/Euler-Vlasov-Fokker-Planck equations.

报告人:王腾(北京工业大学)

Abstract: In this paper, we investigate the wave phenomena to the three-dimensional compressible Navier-Stokes/Euler-Vlasov-Fokker-Planck system (denoted by NS/E-VFP in abbreviation). We show that the planar rarefaction wave is time-asymptotic stable for both NS-VFP and E-VFP systems in 3D. It should be noted that such a wave phenomena has never been observed from the pure Fokker-Planck equation and compressible ?uids with damping term, which was first proved for a fuid-particle model. This work is joint with Professor Hai-liang Li and Professor Yi Wang.

 

时间: 1月14日(周一)16:15-17:00

题目:Asymptotic analysis of the linearized Boltzmann collision operator from angular cutoff to non-cutoff

报告人:何凌冰(清华大学 北京)

Abstract :  In this talk, we will give quantitative estimates on the asymptotics of the linearized Boltzmann collision operator and its associated equation from angular cutoff to non cutoff. On one hand, the results disclose the link between the hyperb

 

时间: 1月15日(周二)8:30-9:15

题目:Stability of basic wave patterns to some kinetic equations

报告人:王益 研究员(中国科学院数学与系统科学院研究院)

Abstract :  We will first talk about the hydrodynamic limit of classical Boltzmann equation to the compressible Euler equations in the setting of 1D generic Riemann solutions which is the superposition of three basic wave patterns, i. e., the shock and rarefaction waves and contact discontinuity. Then we will show the nonlinear stability of these three basic wave patterns to the bipolar Vlasov-Poisson-Boltzmann (VPB) systems which describe the motion of the dilute and charged particles under the effect of bipolar electric fields, based on a new micro-macro type decomposition around the local Maxwellian we established for the bipolar VPB system, and our most recent results on the asymptotic stability of planar rarefaction wave to 3D Boltzmann equation.

 

时间: 1月15日(周二)9:15-10:00

题目:On the spatial decay of the Boltzmann equation with hard potentials

报告人:王海涛(上海交通大学)

Abstract : We study the spatial decay of the solution to the Boltzmann equation with hard potentials for both linear and nonlinear problems. For the nonlinear study, we get the spatial behavior by using the nonlinear weighted energy estimate. This nonlinear result can be viewed as a supplement to the existing wellposedness and time decay results. For the linear problem, we get the space-time pointwise behavior under some slow velocity decay assumption, which extends the classical results from hard sphere to hard potential. Both results reveal that hard sphere and hard potential models differ in their spatial behaviors.

 

时间: 1月15日(周二)10:15-11:00

题目:Global well-posedness for the Boltzmann equation with a class of large amplitude data

报告人:王勇(中国科学院数学与系统科学研究院)

Abstract: In this talk, we will introduce some results on the global well-posedness of Boltzmann for a class of initial data with large amplitude oscillations. It is based on several joint works with Renjun Duan, Feiming Huang, Tong Yang and Zhu Zhang.

 

时间: 1月15日(周二)11:00-11:45

题目:The Behaviors of Solutions to Compressible Navier-Stokes (Euler)- Fokker-Planck Equations

报告人:孙家伟(北京应用物理与计算数学研究所)

Abstract :  We study Cauchy problem of the compressible Navier-Stokes-Fokker-Planck (NSFP) equations and the compressible Euler-Fokker-Planck (EFP) in three dimension. First, we establish the spectrum structures of the linearized  compressible NSFP equations and the linearized  compressible EFP equations respectively. Based on the decay properties of the semigroups of both the linearized compressible NSFP equations and the linearized compressible EFP equations, we prove that the global strong solutions of the Cauchy problem for both the compressible NSFP equations and the compressible EFP equations tend to the equilibrium states at the  optimal time decay rate (1+t)^{-/frac{3}{4}} in L^{2} norm.  Then, we establish the pointwise estimates of the global strong solutions to Cauchy problem of both the compressible NSFP equations and the compressible EFP equations.

地点:首都师范大学本部教二楼 527 教室

联系人:牛冬娟