课程 · Graduate
Fluid Dynamics
From the continuum hypothesis to the regularity theory of the incompressible Navier-Stokes equations.
A mathematical course in fluid dynamics. The first half derives the equations of motion: fields and the material derivative, conservation of mass, vorticity and circulation, the stress tensor, the Euler equations, potential flow, and the incompressible Navier-Stokes equations with their exact solutions and scaling. The second half reads the equations as mathematics: Stokes flow and boundary layers, the vorticity equation and vortex stretching, the energy equality, the Kolmogorov theory of turbulence, the Cauchy problem and the Leray projection, Leray-Hopf weak solutions, regularity criteria and partial regularity.
It is for readers who know multivariable calculus, linear algebra and the basic theory of partial differential equations. Each unit ends with a quiz of computations, conceptual questions and short proofs; the final exam covers the whole course.
之后的来: Partial-Differential-Equations, Multivariable-Calculus, Linear-Algebra
课程
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Describing a flow
3 经验教训 -
Mass, the stream function and vorticity
3 经验教训 -
Stress, pressure and ideal flow
4 经验教训 -
Slow flow and thin layers
2 经验教训 -
Vorticity, energy and turbulence
3 经验教训 -
The Cauchy problem and weak solutions
2 经验教训 -
Regularity and criticality
2 经验教训
期末考试
每个单位的问题,最难回答的问题最后。输入的答案以代数系统为标志;证据和照片工作用模型读取;然后一个人在结果发布之前审查整份文件。通过并获得带有其链接的证书。 通行证: 70%.
签署日期