This seminar is mainly about the theory of unbounded operators and its application to the PDEs and dynamic systems. We are scheduled to begin at mid-July, 2023, where lecture sources and meeting videos will be uploaded in this post.

The course is given by Prof. Liu from Peking university in 2023, some lecture notes can be seen on his main page.

We will introduce the construction of $k-$solitary waves for focusing NLS in enery sub/super/critical cases respectively, and investigate the blowup phenomeon developed by solitons.

The Hilbert transform arises when we investigate $\nabla u $ in the 1D vorticity equation, which behaves similarly as $H\omega$. We will introduce the basic properties of Hilbert transform and apply it to solve ODE containing $H$.