theorem 31.77 Rayleigh's inflexion-point criterion

Rests on

• depends_on theorem 31.22 Euler's equations of motion ¶
  • depends_on definition 31.21 Ideal fluid ¶
    • depends_on definition 31.1 Fluid ¶
      • depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
        • depends_on definition 30.17 Traction ¶
        • depends_on definition 13.5 Tensor under orthogonal transformations ¶
        • proves proof ch:13-continuum-elasticity@proof-7 ¶
  • depends_on lemma 31.11 Transport theorem for a material volume ¶
    • depends_on definition 31.4 Material derivative ¶
      • depends_on equation 7.124 eq:ana-nabla-gradient ¶
      • depends_on proposition 7.104 Chain rule in several variables ¶
        • depends_on definition 7.13 Composite function ¶
        • depends_on definition 7.99 Differentiability at a point ¶
        • depends_on definition 7.102 Differential of a function ¶
        • proves proof ch:05-real-analysis@proof-63 ¶
      • proves proof ch:14-fluid-dynamics@proof-1 ¶
    • depends_on theorem 7.133 Gauss ¶
      • depends_on definition 7.127 Simple regions ¶
        • depends_on definition 7.98 Functions of class $C^{1}$ ¶
        • depends_on definition 6.9 Compact set ¶
      • depends_on remark 7.128 What the derivations below take as given ¶
        • depends_on definition 7.125 Multiple integral ¶
        • depends_on theorem 7.40 Continuous functions are integrable ¶
        • depends_on theorem 7.25 Heine–Cantor: uniform continuity ¶
      • depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
        • depends_on definition 7.41 Antiderivative ¶
        • depends_on theorem 7.42 Fundamental theorem of calculus, I ¶
        • proves proof ch:05-real-analysis@proof-25 ¶
      • proves proof ch:05-real-analysis@proof-79 ¶
    • proves proof ch:14-fluid-dynamics@proof-4 ¶
  • depends_on theorem 30.21 Cauchy's equation of motion ¶
    • depends_on theorem 7.133 Gauss ¶ ↺
    • depends_on theorem 30.18 Cauchy: the stress tensor exists ¶ ↺
    • proves proof ch:13-continuum-elasticity@proof-9 ¶
  • proves proof ch:14-fluid-dynamics@proof-11 ¶
• depends_on theorem 31.58 The vorticity transport equation ¶
  • depends_on equation 31.5 eq:fluid-curl-cross ¶
  • depends_on theorem 31.37 The Navier–Stokes equations ¶
    • depends_on theorem 31.36 The Newtonian constitutive relation ¶
      • depends_on definition 31.32 Newtonian fluid; dynamic and kinematic viscosity ¶
        • depends_on definition 31.1 Fluid ¶ ↺
        • depends_on definition 31.8 Rate of strain and vorticity ¶
      • depends_on proposition 31.9 Cauchy–Stokes decomposition ¶
        • depends_on definition 31.8 Rate of strain and vorticity ¶ ↺
        • proves proof ch:14-fluid-dynamics@proof-3 ¶
      • proves proof ch:14-fluid-dynamics@proof-17 ¶
    • depends_on theorem 31.22 Euler's equations of motion ¶ ↺
    • proves proof ch:14-fluid-dynamics@proof-18 ¶
  • proves proof ch:14-fluid-dynamics@proof-27 ¶
• proves proof ch:14-fluid-dynamics@proof-38 ¶

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