报告题目： Global weak solutions to the isentropic compressible Navier-Stokes equations with vacuum and unbounded density in a half-plane under Dirichlet boundary conditions
报告人：钟新教授
报告时间：10月15日下午13：30-14：30
腾讯会议：197-772-289
报告摘要：We establish the global existence of a class of weak solutions to the isentropic compressible Navier-Stokes equations in a half-plane with Dirichlet boundary conditions, allowing for vacuum both in the interior and at infinity, under a suitably small initial total energy. The solutions constructed here admit unbounded densities and lie in an intermediate regularity regime between the finite-energy weak solutions of Lions-Feireisl and the framework of Hoff. This result generalizes previous works of Hoff (Comm. Pure Appl. Math. 55 (2002), pp. 1365-1407) and Perepelitsa (Arch. Ration. Mech. Anal. 212 (2014), pp. 709-726) concerning discontinuous solutions by allowing vacuum states and unbounded density. Our analysis relies on the Green function method and new estimates involving the specific structure of the equations and the geometry of the half-plane. To the best of our knowledge, this is the first result concerning global weak solutions within Hoff's framework on an unbounded domain that simultaneously accommodates Dirichlet boundary conditions and far-field vacuum. The intermediate-regularity class developed here may be viewed as a natural extension of Hoff's theory, precisely tailored to overcome the two corresponding obstructions: the lack of global space-time control of the effective viscous flux arising from far-field vacuum and the absence of boundary-induced regularity gains in the no-slip setting.
个人简介：钟新，西南大学数学与统计学院教授，博士生导师，副院长，学院和学部学术委员会委员。主要研究领域为可压缩Navier–Stokes 方程组及相关模型解的定性理论，部分成果以独立作者或通讯作者发表于Math. Ann.、J. Math. Pures Appl.、Comm. Partial Differential Equations、Indiana Univ. Math. J.、J. Nonlinear Sci.、Calc. Var. Partial Differential Equations等期刊上，主持国家自然科学基金项目3项、省部级科研项目7项。曾先后入选重庆市巴渝学者青年学者、重庆英才青年拔尖人才，获得重庆市自然科学奖三等奖(独立完成人)、萧文灿数学杰出教师奖。
