Mathematical Sciences: The Partial Differential Equations ofFluid Dynamics and their Numerical Approximation

PI将继续他的研究计划， 多方向流体动力学微分方程 包括可压缩和不可压缩的流动。 作为 主要目标，他将重点关注以下四个主题： 1. 经典弱解与测度值 不可压缩欧拉方程的解 在二维和三维空间中。 2. 三维Euler方程光滑解的分解 方程 3. 多维守恒定律和几何 冲击动力学 4. 超音速飞行器不稳定性的非线性发展 剪切层 本文的研究属于应用非线性力学的一般范畴 分析是目前一个重要的和活跃的研究 应用数学领域。 分析和 研究问题的数值解法 提高了研究项目的成功潜力。 一 可以预期该计划的研究结果具有重要意义 对数学科学界和 一般科学和工程界。

The PI will continue his research program on partial differential equations of fluid dynamics in several directions involving both compressible and incompressible flows. As primary goals, he will focus on the following four topics: 1. Classical weak solutions and measure-valued solutions of the incompressible Euler equations in 2 and 3 dimensions. 2. Breakdown of smooth solutions for the 3-D Euler equations. 3. Multi-dimensional conservation laws and geometric shock dynamics. 4. Nonlinear development of instabilities in supersonic shear layers. The research is in the general area of applied nonlinear analysis which is currently an important and active research area of applied mathematics. The mixture of analytical and numerical approaches to the solutions of research problems enhances the success potential of the research program. One can expect research results from the program with significant impact on both the mathematical science community and the general science and engineering community.