报告题目：Energy equality in the Naiver-Stokes equations
报告人：王艳青博士（郑州轻工业大学）
时间：2021年9月8日，上午9：30-11：30
腾讯会议：445 666 484
摘要：In this talk, first, we present a new energy conservation criteria via a combination of velocity and its gradient for weak solutions of the general compressible Navier-Stokes equations with bounded density with positive lower bound. This helps us to extend the conditions via the velocity or gradient of the velocity for energy equality from the incompressible fluid to compressible flow and improves the recent results due to Nguyen-Nguyen-Tang [Nonlinearity 32 (2019)]and Liang [Proc. Roy. Soc. Edinburgh Sect. A (2020)]. Second, it is shown that classical Lions's condition for energy balance in the incompressible fluid is also valid for the weak solutions of the isentropic compressible Navier-Stokes equations allowing vacuum under suitable integrability conditions on the density and its derivative. This allows us to establish various sufficient conditions implying energy equality for the compressible flow. This is an improvement of corresponding results obtained by Yu in [32, Arch. Ration. Mech. Anal., 225 (2017)], and our criterion via the gradient of the velocity partially answers a question posed by Liang in [18, Proc. Roy. Soc. Edinburgh Sect. A (2020)].
报告人简介：王艳青，博士，郑州轻工业大学77779193永利官网教师，硕士生导师。主要从事流体力学方程弱解正则性和能量守恒的数学研究，相关论文发表在Nonlinearity、JDE、PJM、JMFM等杂志上。
