学术报告 报告题目1：Incompressible Limit of isentropic Navier-Stokes equations with Navier-slip boundary
报 告 人：熊林杰 博士（湖南大学）
报告时间：2017年06月09日（星期五）下午14：30-15：30
报告题目2：Nonlinear stability of relativistic vortex sheets in two spatial dimensions
报 告 人：王涛 博士（武汉大学）
报告时间：2017年06月09日（星期五）下午15：30-16：30
报告地点：4号楼4318室
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数学学院
2017年06月07日
报告1摘要：
This talk concerns the low Mach number limit of weak solutions to the compressible Navier-Stokes equations for isentropic fluids in a bounded domain with a Navier-slip boundary condition. It has been proved that if the velocity is imposed the homogeneous Dirichlet boundary condition, as the Mach number goes to 0, the velocity of the compressible flow converges strongly in $L^2$ under the geometrical assumption (H) on the domain. We justify the same strong convergence when the slip length in the Navier condition is the reciprocal of the square root of the Mach number.
报告2摘要：
We study vortex sheets for the relativistic Euler equations in three-dimensional Minkowski spacetime. The problem is a nonlinear hyperbolic problem with a characteristic free boundary. The so-called Lopatinskii condition holds only in a weak sense, which yields losses of derivatives. A necessary condition for the weak stability is obtained by analyzing roots of the Lopatinskii determinant associated to the linearized problem. Under such stability condition, we prove short-time existence and nonlinear stability of relativistic vortex sheets by a Nash-Moser iterative scheme. This talk is based on a joint work with Prof. Gui-Qiang Chen (Oxford) and Prof. Paolo Secchi (Brescia)