코스 · 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.
다음에 오는: Partial-Differential-Equations, Multivariable-Calculus, Linear-Algebra
코스에 대해
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Describing a flow
3 레슨 -
Mass, the stream function and vorticity
3 레슨 -
Stress, pressure and ideal flow
4 레슨 -
Slow flow and thin layers
2 레슨 -
Vorticity, energy and turbulence
3 레슨 -
The Cauchy problem and weak solutions
2 레슨 -
Regularity and criticality
2 레슨
마지막 시험
모든 단위에서 질문, 가장 어려운 것들 마지막. 입력 답변은 대수학 시스템에 의해 표시됩니다; 증거와 사진 작업 모델에 의해 읽어; 그럼 사람이 결과가 발표되기 전에 전체 종이를 검토. 통과하고 자신의 링크와 함께 인증서를 얻을. 통과 표시: 70%.
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