Mathematical Problems in Fluid Dynamics

[101022]近年来，关于拉格朗日粒子分析的理论兴趣和实验努力不断增加。提出的研究是发展欧拉-拉格朗日方法最近才开始。这种方法的一个主要研究对象是允许自然公式的扩散拉格朗日路径逆，包括无粘柯西公式的粘性模拟。该解决方案是使用恒等变换附近的乘积展开来构建的。建议研究这种结构，并将其应用于随机强迫流动。此外，还提出了紊流燃烧中强随机流对火焰的猝灭研究。流体和等离子体表现出许多活跃的运动尺度，并且众所周知难以精确计算和预测。原因是描述它们的方程还没有被很好地理解。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