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12月17日下午15:00--16:00 综合楼1116 施小丁 Exponential Decay for Lions-Feireisl's Weak Solutions to the Barotropic Compressible Navier-Stokes Equations in 3D Bounded Domains

 

报告题目:Exponential Decay for Lions-Feireisl's Weak Solutions to the Barotropic Compressible Navier-Stokes Equations in 3D Bounded  Domains

报告人:施小丁教授 (北京化工大学数理学院)

报告时间:12月17日下午15:00--16:00

地点:阜成路西区综合楼1116会议室

报告人简介:

  施小丁,北京化工大学教授。博士毕业于中国科学院数学与系统科学研究院,曾在日本大阪大学从事博士后研究。主要研究流体力学方程,包括可压缩Navier-Stokes方程组的冲击波、稀疏波、接触间断和边界层以及各种波的叠加、碰撞的大时间行为。非牛顿不可压缩Navier-Stokes方程组固液耦合问题和混合边值问题解的存在性、稳定性及数值分析。两相流Navier-Stokes-Cahn-Hilliard方程组、Navier-Stokes-Allen-Cahn方程组的解的适定性、大时间行为以及扩散界面极限问题等。部分成果发表在数学领域著名杂志Comm. Math. Phys., SIAM J. Math. Anal., Indiana Univ. Math. J., Nonlinearity,J. Differential Equations.等。多次主持国家自然科学基金项目。

报告摘要:

  In this talk, we will consider the barotropic compressible Navier-Stokes equations in three-dimensional (3D) bounded domains, we prove that any finite energy weak solution  obtained by  Lions [Mathematical topics in fluid mechanics, Vol. 2. Compressible models(1998)] and Feireisl-Novotny-Petzeltova [J. Math. Fluid Mech. 3(2001), 358-392]  decays exponentially to the equilibrium state. This result is established by both using the extra integrability of the density due to Lions and  constructing a suitable Lyapunov functional just under the framework of Lions-Feireisl's weak solutions.