Mathematical Sciences: Nonlinear Partial Differential Equations and Fluid Dynamics and Mechanics

这是一个研究冲击波和其他 不连续的解决方案的方程，支配流动的 可压缩流体比如，还有很多没有答案的 关于耗散机制在 两个或多个冲击波的相互作用和长时间的 这种波浪的稳定性 主要研究者将使用 分析和渐近工具来回答这些问题， 相关的。 除了通常的流体方程 动力学的主要研究者将研究系统的 磁流体力学方程，气体动力学理论， 以及浅水波理论 在某些情况下，摩擦力等耗散力可能很小， 流体动力学中的一些问题，但它们的影响不可忽视。 例如，气体的粘度（内部摩擦）非常小。 小，但它会影响物体的大尺度行为， 穿过气体。 首席研究员将研究如何 这种小的耗散机制可以影响形成， 冲击波在气体中的传播 冲击波是一种 就像音爆一样，这是气流的一个重要特征， 高速。

This is a project to study shock wave and other discontinuous solutions of the equations that govern the flow of compressible fluids. For example, there are still many unanswered questions regarding the role that dissipative mechanisms play in the interaction of two or more shock waves and the long-time stability of such waves. The principal investigator will use analytic and asymptotic tools to answer these questions and related ones. In addition to the usual equations of fluid dynamics the principal investigator will study systems of equations in magneto-hydrodynamics, the kinetic theory of gases, and the theory of shallow water waves. Dissipative forces like friction can be small in certain problems in fluid dynamics, but their effect cannot be neglected. For example, the viscosity (internal friction) of a gas is very small and yet it affects the large-scale behavior of objects that move through the gas. The principal investigator will study how such small dissipative mechanisms can influence the formation and propagation of shock waves in gases. A shock wave is something like a sonic boom, and it is an important feature of flows at high speeds.