学术报告报告题目：Global well-posedness of the nematic liquid crystal flows with vacuum
报 告 人：刘洋 博士（南京大学）
报告时间：2018年7月6日（周五）上午9:30 – 10:10
报告地点：4号楼4224室
邀 请 人：温焕尧 教授
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数学学院
2018年7月5日
报告摘要：
In this talk, we consider a simplified version of the Ericksen-Leslie model, which a strongly coupled system between the nonhomogeneous incompressible Navier-Stokes equations and the transported heat flows of harmonic map. In the case that viscosity µ is a constant, we prove that there exists a unique global strong solution on R3 without additional compatibility condition, under assuming that the basic energy is small enough, which extend the result by Li(MAA,2015) to the whole space. Moreover, when the viscosity coefficient is a function of the density of fluid, global well-posedness of strong solutions with large oscillations is established in a smooth bounded domain Ω ⊂ R3, provided k∇u0kL2 +k∆d0kL2 is suitably small with arbitrary large initial density, which extended the local strong solution by Gao et al. (JDE, 2016) to be a global one.