theorem A.707 D'Alembert's paradox

Rests on

• depends_on proposition 31.28 Potential flow reduces to Laplace's equation ¶
  • depends_on corollary 31.13 Incompressible flow ¶
    • depends_on theorem 31.12 Conservation of mass ¶
      • depends_on lemma 31.11 Transport theorem for a material volume ¶
        • depends_on definition 31.4 Material derivative ¶
        • depends_on theorem 7.133 Gauss ¶
        • proves proof ch:14-fluid-dynamics@proof-4 ¶
      • proves proof ch:14-fluid-dynamics@proof-5 ¶
    • proves proof ch:14-fluid-dynamics@proof-6 ¶
  • depends_on equation 10.24 eq:pde-poisson-equation ¶
  • depends_on proposition 7.136 Properties of conservative fields ¶
    • depends_on definition 7.135 Conservative field ¶
      • 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 7.9 Real function ¶
      • depends_on definition 7.99 Differentiability at a point ¶
        • depends_on definition 7.16 Limit ¶
        • depends_on definition 5.37 Linear transformation ¶
        • depends_on equation 6.12 eq:top-euclidean-metric ¶
      • depends_on definition 7.102 Differential of a function ¶
        • depends_on definition 7.99 Differentiability at a point ¶ ↺
        • depends_on definition 7.97 Partial derivative; gradient ¶
      • proves proof ch:05-real-analysis@proof-63 ¶
    • depends_on theorem 7.132 Stokes ¶
      • depends_on proposition 7.104 Chain rule in several variables ¶ ↺
      • depends_on proposition 7.105 Clairaut–Schwarz ¶
        • depends_on definition 7.20 Continuity at a point ¶
        • depends_on theorem 7.35 Mean value theorem ¶
        • proves proof ch:05-real-analysis@proof-64 ¶
      • depends_on theorem 7.131 Green ¶
        • depends_on definition 7.127 Simple regions ¶
        • depends_on remark 7.128 What the derivations below take as given ¶
        • depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
        • proves proof ch:05-real-analysis@proof-77 ¶
      • proves proof ch:05-real-analysis@proof-78 ¶
    • proves proof ch:05-real-analysis@proof-80 ¶
  • proves proof ch:14-fluid-dynamics@proof-14 ¶
• depends_on theorem 31.24 Bernoulli ¶
  • depends_on equation 31.4 eq:fluid-lamb-identity ¶
  • 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 lemma 31.11 Transport theorem for a material volume ¶ ↺
    • 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 ¶
  • proves proof ch:14-fluid-dynamics@proof-12 ¶
• proves proof app:A-long-proofs@proof-418 ¶

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