报告题目：Global smooth solutions to the compressible Euler equations for Chaplygin gas and related models

报  告 人：王玉柱教授（华北水利水电大学）

报告时间：12月6日下午4:00--5:00.

报告地点：广东工业大学龙洞校区行政楼607

主  持 人：翟小平

摘要：In this topic, global smooth solutions to compressible Euler equations for Chaplygin gases and are investigated. For three dimensional Chaplygin gases, based on the new formulation of the compressible Euler equations introduced by J. Luk and J. Speck, we first show that the wave system satisfied by the modified density and the velocity for Chaplygin gases verifies the weak null condition. Then we can prove the global existence of the smooth solutions to the irrotational and isentropic Chaplygin gases without introducing the potential function when the initial data are prescribed as small perturbations to the given constant state. For two dimensional compressible Euler equations with the rotational Coriolis forcing, global smooth solutions are established under the assumption of small data and zero relative vorticity. The proof is based on the effect of Klein-Gordon equations, the ghost weight energy estimate and the bootstrap argument.

王玉柱简介：教授、博士生导师、河南省高层次人才、河南省优秀青年科技专家、华北水利水电大学“大禹学者”特聘教授。2010年毕业于上海交通大学数学系，获理学博士学位。主要从事非线性偏微分方程及其应用的研究，在Comm.Partial Differential Equation、J.Differential Equations等期刊上发表论文50余篇。主持国家自然科学基金项目面上项目和青年项目、河南省科技创新杰出青年项目、河南省高校科技创新人才支持计划及河南省高校重点科研项目基础研究专项等项目。主持获河南省科学技术进步二等奖和河南省自然科学三等奖各1项、参与获浙江省自然科学二等奖和河南省科学技术进步三等奖各1项。