Mathematical Problems in Fluid Dynamics

0101022 Constantin关于拉格朗日粒子分析的理论兴趣和实验努力在过去几年中一直在增加。拟议的研究是开发一个欧拉-拉格朗日方法最近开始。在这种方法中的一个主要研究对象是一个扩散拉格朗日路径逆，允许一个自然的配方，包括粘性模拟的无粘柯西公式。该解决方案是使用接近恒等变换的乘积展开来构建的。建议研究这种构造并将其应用于随机强迫流。此外，还提出了湍流燃烧中强随机流对火焰熄灭的研究。流体和等离子体表现出许多活跃的运动尺度，众所周知，很难精确计算和预测。原因是描述它们的方程还没有被很好地理解。本文提出用数学方法研究极端条件下动量和热量的输运过程

0101022ConstantinTheoretical interest and experimental efforts concerning Lagrangian particle analysis have been increasing in the last years. The proposed research is to develop an Eulerian-Lagrangian approach initiated very recently. A main object of study in this approach is a diffusive Lagrangian path inverse that allows a natural formulation, including a viscous analogue of the inviscid Cauchy formula. The solution is built using a product expansion near the identity transformation. It is proposed to study this construction and apply it to randomly forced flows. In addition, the study of quenching of flames by strong random flows in turbulent combustion is proposed.Fluids and plasmas exhibit many active scales of motion, and are notoriously difficult to compute and predict accurately. The reason is that the equations describing them are not well understood. It is proposed to study mathematically the processes of transport of momentum and heat under extreme conditions