报告题目：**Classical finite energy solutions to compressible Navier-Stokes equations**
报告时间：2016年7月13日(周三)下午15:00-16:00
报告地点：数理楼3层数学研究所对面学术报告厅(2315-3)
报告人：**Prof. Ronghua Pan** (Georgia Institute of Technology美国佐治亚理工学院)
摘要：The local existence of classical solutions to Cauchy problem of compressible Navier-Stokes with finite total energy encounters the strong degeneracy of evolution and viscosity, in particular, when the viscosity coefficients depend on density in a power law. In the talk, I will discuss some previous results, and the recent results we obtained in this direction. This talk is based on my joint works with Y. Li and S. Zhu.
报告题目：**$L^2$-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws**
报告时间：2016年7月13日(周三)下午16:00-17:00
报告地点：数理楼3层数学研究所对面学术报告厅(2315-3)
报告人：**王益****研究员** (中国科学院数学与系统科学研究院)
摘要：We consider $L^2$ contraction of large viscous shock wave for the multi-dimensional scalar viscous conservation laws, up to a suitable shift. The shift function depends on both time and space variable, which solves a parabolic equation with inhomogeneous coefficient reflecting the perturbation. We consider a suitably small $L^2$-perturbation around a viscous planar shock wave of arbitrarily large strength. However, we do not impose any conditions on the anti-derivative variables of the perturbation around shock profile. More precisely, it is proved that if the initial perturbation around the viscous shock wave is suitably small in $L^2$ norm, then $L^2$ contraction holds true for the viscous shock wave up to a shift function which may depend on the temporal and spatial variables. Moreover, as the time $t$ tends to infinity, the $L^2$ contraction holds true up to a time-dependent shift function. In particular, if we choose some special initial perturbation, then we can prove a $L^2$-convergence of perturbation towards shock profile up to a time-dependent shift. It is a joint work with Alexis Vasseur from University of Texas at Austin (USA) and Moon-Jin Kang from Seoul National University (Korea).
**欢迎参加！**
联系人：王术、黎勇 |