Analysis Seminar

今後の予定

会場: 九州大学伊都キャンパスウエスト1号館 5階 C504室小講義室
講演者: 髙橋知希氏（和歌山工業高等専門学校）
題目: Spatial pointwise behavior of gradient of Navier-Stokes flow around a rigid body moving by time-periodic motion, with application to stability of time periodic flow
要旨: We consider the spatial pointwise behavior of time-periodic solutions to the Navier-Stokes equation in the exterior of a rigid body, moving by time-periodic motion. For the translational and angular velocity of the body, assuming besides smallness and regularity, either of the following conditions: (i) translation or rotation is absent; (ii) both velocities are parallel to the same constant vector. If time average over a period of translational velocity, \(\lambda\) (say), is non-zero (resp. zero), we then show that gradient of the velocity of the fluid decays like the one of the gradient of the Oseen fundamental solution (resp. decays at the rate \(O(|x|^{－2})\)). In the case \(\lambda\ne 0\), we apply them to the stability of the time-periodic solution for small data to deduce sharp convergence properties.