Abstract:
The Eulerian dynamics describes many interesting phenomena in fluid mechanics. In this talk, I will discuss several equations that lie in this catergory, including the damping Burgers equation, the Euler-Poisson equation and the Euler-Alignment equation. Though a lot of work has been done for the problems in one-dimension, much less is known in multi-dimensions, due to the effect of the "spectral gap". I will explain the main difficulty of controling the spectral gap, and introduce a new way to handle the term in the case when the solution is radially symmetric. |