报告人：Joachim Escher 教授（德国Leibniz University Hannover副校长）

报告题目： The Rayleigh-Taylor Condition for the Muskat Problem

报告摘要：Of concern is the moving boundary problem of a two-phase potential flow of two fluids with possible different densities and viscosities. Such problems are known as Muskat problems or two-phase Hele-Shaw flows. Due to the moving interfaces these problems are intrinsically nonlocal and highly nonlinear. A criterion is presented, known as the generalised Rayleigh-Taylor condition, which guarantees that for large classes of initial data these problems are classically well-posed, possibly on a finite time interval only . Away from the Rayleigh-Taylor regime the system becomes unstable and finger-shaped unstable steady states can occur. A thin film approximation is also discussed. Here the dynamical behaviour is different: global weak solutions exist for any square integrable non-negative initial configuration. In addition, the flat steady state is globally stable in the class of weak solutions.

报告人简介：Joachim Escher 教授是国际著名数学家，德国汉诺威大学应用数学所的首席教授（Chair Professor），目前担任德国汉诺威大学副校长，主管国际交流。Joachim Escher 教授在非线性偏微分方程及相关领域科研成果卓著，已出版《Analysis》专著1-3 卷，在数学四大顶级期刊Acta Mathematica和Annals of Mathematics，以及CPAM,  CMP,  ARMA与Adv. Math等一流期刊上发表SCI论文160 多篇。Joachim Escher 教授目前正担任Nonlinear Analysis: Real World Applications 的主编，曾担任SIAM Journal on Mathematical Analysis，Nonlinear

Analysis，Journal of Evolution Equations，Monatshefte für Mathematik 等多个SCI 数学期刊的编委。

报告时间：2019年5月5日（星期日）上午10:30

报告地点：科技楼南楼702室