## Differential Equations Seminar

#### Dr. Jing Tian, Towson University

**Title:**Analysis of attractors and chaos for certain models in fluids and wave propagation

**Abstract:**In this talk, there are two topics being discussed. One topic is related to a turbulence model in fluids. Another is related to the Chaotic phenomenon in wave propagation.

The first topic is On the emergence of the Navier-Stokes-alpha model for channel flows. In this study, we concentrate our consideration to a restricted class of fluid flows. With the hypothesis that the turbulence described by the NS-alpha is partly due to the roughness of the walls, we present the transition from the Navier-Stokes equations into the Navier-Stokes-alpha model by introducing a Reynolds type averaging.

The second topic is the study of Chaotic Vibration of the Wave Equation in 2D. Chaotic vibration has been studied by many mathematicians and engineers in the literature. However, almost all those studies are either on ODEs or about the 1D wave equation. In this study, by designing some numerical simulations, we study the Chaotic Phenomenon in 2D wave equation.