偏微分方程研讨班：The global stability of large Fourier mode for 3-D Navier-Stokes equations in the cylindrical coordinates

中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：刘彦麟（北京师范大学）  

题  目：The global stability of large Fourier mode for 3-D Navier-Stokes equations in the cylindrical coordinates (I)

时  间：2023.06.18（星期日）10:00-11:00

地  点：腾讯会议号：376-108-310

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题  目：The global stability of large Fourier mode for 3-D Navier-Stokes equations in the cylindrical coordinates (II)

时  间：2023.06.24（星期六）10:00-11:00

地  点：腾讯会议：376-108-310

摘 要：We intend to study 3-D incompressible Navier-Stokes equations in the cylindrical coordinates. Here we do not limit us in the classical axisymmetric case, but the axisymmetric structure still plays a key role. For general initial data, we can expand them into Fourier series in $\theta$ variable. In particular, we prove the global existence of strong solutions if the initial data is of the form: $A(r,z)\cos N\theta +B(r,z)\sin N\theta$, provided that $N$ is large enough. This is based on joint works with Ping Zhang.