Analysis of Viscoelastic Flows

聚合物液体中流动问题的研究对数学分析提出了许多挑战。本项目的研究课题包括粘弹性流动的可控性、全局稳定性和动力学、液体射流破碎的渐近分析、乳状液复杂流动的数值模拟、以及通过障碍物的高Weissenberg数渐近性。粘弹性流动的应用出现在塑料、食品和其他产品的制造以及血液流动等生物问题中。在该项目下进行的研究将澄清基本问题，以便更好地了解这些流动并制定模拟方法。

The study of flow problems in polymeric liquids poses numerous challenges for mathematical analysis. The topics addressed in this project include controllability of viscoelastic flows, global stability and dynamics, asymptotic analysis of the breakup of liquid jets, numerical simulation of complex flows of emulsions, and high Weissenberg number asymptotics of flow past an obstacle.Applications of viscoelastic flows arise in manufacturing of plastics, foods and other products, as well as in biological problems such as blood flow. The research carried on under this project will clarify fundamental issues to enable a better understanding of these flows and the development of methods for their simulation.