Schedules of future seminars
● 2017 年 6 月 16 日 15:30 〜 17:30
- 佐川 侑司 氏 （大阪大学理学研究科）
Yuji Sagawa (Osaka University)
● 2017 年 6 月 23 日 14:45 〜 16:45
- 阿部 健 氏 （大阪市立大学理学研究科）
Ken Abe (Osaka City University)
- Global well-posedness of the two-dimensional exterior Navier-Stokes equations for non-decaying data
We consider the two-dinsosional Navies-Stokes equations in an exterior domain,
subject to the Dirichlet boundary condition.
Stationary solutions of this problem and their asymptotic behavior have been studied in a large literature,
while a few results are known about the non-stationary problem for non-decaying initial data.
We report some global well-posedness result for bounded initial data with a finite Dirichlet integral,
and unique existence of asymptotically constant solutions for arbitrary large Reynolds numbers.
● 2017 年 6 月 30 日 15:30 〜 17:30
- 水町 徹 氏 （広島大学理学研究科）
Tetsu Mizumachi (Hiroshima University)
- Asymptotic linear stability of the Benney-Luke equation in 2D
We study transverse linear stability of line solitary waves to the 2-dimensional Benney-Luke equation which arises in the study of small amplitude long water waves in 3D.
In the case where the surface tension is weak or negligible, we find a curve of resonant continuous eigenvalues near 0.
Time evolution of these resonant continuous eigenmodes is described by a 1D damped wave equation in the transverse variable
and it gives a linear approximation of the local phase shifts of modulating line solitary waves.
In exponentially weighted space whose weight function increases in the direction of the motion of the line solitary wave,
the other part of solutions to the linearized equation decays exponentially as $t\to\infty$.