Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	牛冬娟教授, 首都师范大学
Inviter:	曹道民研究员
Title:	Some progress on incompressible flows with helical symmetry
Language:	Chinese
Time & Venue:	2023.06.14 10:00-11:00 南楼602
Abstract:	Helical symmetry is invariance under a one-dimensional group of rigid motions generated by a simultaneous rotation around a fixed axis and translation along the same axis. In this talk, we mainly investigate the following two questions: 1) we are concerned with the vanishing viscosity problem for the three-dimensional Navier-Stokes equations with helical symmetry in the whole space. A new decomposition of a helical vector field is introduced to make it available to obtain uniform estimates of the vorticity; 2) we prove that the weak solutions of the three-dimensional incompressible Euler equations with helical symmetry in the whole space exist when the initial vorticity lies in L1∩Lp with p>1. The key ingredient here involves the explicit analysis of Biot-Savart law with helical symmetry in domain R2×[?π, π] via the theories of singular integral operators and second order elliptic equations. In particular, the assumption with vanishing helical swirl is necessary.