Mathematical Problems in Fluid Dynamics

关于拉格朗日粒子分析的理论兴趣和实验工作在过去几年里一直在增加。拟议的研究是为了发展最近开始的欧拉-拉格朗日方法。这种方法的一个主要研究对象是扩散拉格朗日路径逆，它允许自然的公式，包括无粘柯西公式的粘性类似物。该解决方案是使用身份转换附近的产品扩展构建的。有人建议研究这种结构，并将其应用于随机强迫流动。此外，还提出了湍流燃烧中强随机流对火焰熄灭的研究。流体和等离子体显示出许多活跃的运动标度，并且众所周知，很难准确地计算和预测。原因是描述它们的方程式没有被很好地理解。建议对极端条件下的动量和热量的传输过程进行数学研究。

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