コース · 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.
後に来る: Partial-Differential-Equations, Multivariable-Calculus, Linear-Algebra
コース
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Describing a flow
3 レッスン -
Mass, the stream function and vorticity
3 レッスン -
Stress, pressure and ideal flow
4 レッスン -
Slow flow and thin layers
2 レッスン -
Vorticity, energy and turbulence
3 レッスン -
The Cauchy problem and weak solutions
2 レッスン -
Regularity and criticality
2 レッスン
卒業試験
ユニットごとに問題があり、最も難しい問題が残ります。タイプした答えは代数システムでマークされ、証明と写真の作業はモデルによって読まれ、その後、結果を公開する前に人が全ての論文をレビューします。合格すると、リンク付きの証明書を受け取ります。 合格点: 70%.
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