Studying the Behavior of Von Karman Flow

The von Karman flow plays an important role in mathematics, mechanics and physics. The system governing the motion of the von Karman flow is linearly degenerate in the sense of Lax, and for general initial data, the system loses the property of strict hyperbolicity. Over past centuries, important results have been obtained for classical fluid dynamics. However, little is known about the von Karman flow. The main difficulty is that the partial differential equations for such flow are nonlinear and linearly degenerate. Singularities may form in such systems. In this project, the researchers propose to study the behaviour of von Karman flow, to examine the formation and propagation of singularities in the von Karman flow and to understand the mechanism of formation of singularities. A deep understanding of the behaviour the von Karman flow will have great significance in modern mathematics and physics.