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数学学科现代分析及其应用研究所(温焕尧 华南理工大学)

发布者:戴 情   发布时间:2021-11-30  浏览次数:193

题目1: On global solutions to the viscous liquid–gas model with unconstrained transition to single-phase flow in one dimension

时间:2021年12月7日 9:00-11:00

报告人:温焕尧 华南理工大学教授

地点: #腾讯会议296-338-989

摘要:We consider the Dirichlet problem of a one-velocity viscous drift-flux model in one dimension. By relying on weak compactness tools we obtain an existence result within the class of weak solutions. An essential novel aspect of this analysis, compared to previous works on the same model, is that the solution space is large enough to allow for transition to single-phase flow without any constraints. In particular, one of the phases can vanish in a point while the other phase can persist. The key to achieve this result, which represents a major step forward compared to previous results for this model, is that we do not rely on any higher-order (i.e. derivatives in space) estimates on the masses or pressure, only low-order estimates provided by the energy equality and the uniform upper bounds on the liquid and gas mass. This is joint with Professors Steinar Evje and Changjiang Zhu.

 

题目2:On global solutions to a viscous compressible two-fluid model with unconstrained transition to single-phase flow in three dimensions


时间:2021年12月7日14:00-15:00

报告人:温焕尧 华南理工大学教授

地点: #腾讯会议:646-388-838


摘要:We consider the Dirichlet problem of a viscous compressible two-fluid model in three dimensions. Under weak assumptions on the initial data which can be discontinuous, unbounded and large as well as involve transition to pure single-phase points or regions, we show existence of global weak solutions with finite energy. The essential novelty of this work, compared with previous works on the same model, is that transition to each single-phase flow is allowed without any constraints between adiabatic constants or two densities.  


报告人简介:温焕尧,男,华南理工大学数学学院教授、博士生导师、副院长。目前担任广东省青年科学家协会副会长和华南理工大学党外知识分子联席会副会长。主要从事流体力学中的偏微分方程的数学理论研究。研究成果发表在Adv. Math.Arch. Rational Mech. Anal.CVPDEsJ. Functional AnalysisJ.  Math. Pures Appl.Math. Models Meth. Appl. Sci.SIAM J. Math. Anal.等杂志。先后主持国家自然科学基金青年项目、面上项目和优秀青年科学基金项目。2016-2019年获聘广东省青年珠江学者。   

 

  

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