Vorticity and incompressible flow
Vorticity and incompressible flow
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发表时间：
2001
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通讯作者：
A. Majda;A. Bertozzi
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作者：
A. Majda;A. Bertozzi
序言1.不可压缩流体流动的涡旋动力学介绍2。欧拉方程和纳维尔-斯托克斯方程的涡量流公式3.欧拉和Navier-Stokes方程的能量方法4.用质点轨道法证明欧拉方程解的存在唯一性5.寻找三维欧拉方程的奇异解6.计算涡流方法7.细长涡丝的简化渐近方程8。L9中具有初始涡量的二维Euler方程的弱解。介绍欧拉方程的涡面、弱解和近似解序列10。弱解和二维解序列11.二维欧拉方程：浓度和弱解与涡面初始数据12.减少Hausdorff维数，振荡和测量值的解决方案的欧拉方程在二维和三维13.将Vlasov-Poisson方程作为一个类比，用于研究Euler方程的弱解索引。
Preface 1. An introduction to vortex dynamics for incompressible fluid flows 2. The vorticity-stream formulation of the Euler and the Navier-Stokes equations 3. Energy methods for the Euler and the Navier-Stokes equations 4. The particle-trajectory method for existence and uniqueness of solutions to the Euler equation 5. The search for singular solutions to the 3D Euler equations 6. Computational vortex methods 7. Simplified asympototic equations for slender vortex filaments 8. Weak solutions to the 2D Euler equations with initial vorticity in L 9. Introduction to vortex sheets, weak solutions and approximate-solution sequences for the Euler equation 10. Weak solutions and solution sequences in two dimensions 11. The 2D Euler equation: concentrations and weak solutions with vortex-sheet initial data 12. Reduced Hausdorff dimension, oscillations and measure-valued solutions of the Euler equations in two and three dimensions 13. The Vlasov-Poisson equations as an analogy to the Euler equations for the study of weak solutions Index.