remark 31.69 The Kutta condition, and where the circulation comes from

Rests on

• depends_on corollary 31.65 Lagrange: an irrotational flow stays irrotational ¶
  • depends_on theorem 31.59 Helmholtz's vortex theorems ¶
    • depends_on theorem 31.64 Kelvin's circulation theorem ¶
      • depends_on definition 31.63 Circulation ¶
        • depends_on definition 31.8 Rate of strain and vorticity ¶
        • depends_on theorem 7.132 Stokes ¶
      • depends_on theorem 31.22 Euler's equations of motion ¶
        • depends_on definition 31.21 Ideal fluid ¶
        • depends_on lemma 31.11 Transport theorem for a material volume ¶
        • depends_on theorem 30.21 Cauchy's equation of motion ¶
        • proves proof ch:14-fluid-dynamics@proof-11 ¶
      • proves proof ch:14-fluid-dynamics@proof-29 ¶
    • 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 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-28 ¶
  • depends_on theorem 31.64 Kelvin's circulation theorem ¶ ↺
  • proves proof ch:14-fluid-dynamics@proof-30 ¶
• depends_on theorem 31.68 Kutta–Joukowski ¶
  • depends_on lemma 31.67 Blasius' force formula ¶
    • depends_on theorem 8.6 Cauchy–Riemann equations ¶
      • depends_on definition 7.98 Functions of class $C^{1}$ ¶
        • depends_on definition 7.20 Continuity at a point ¶
        • depends_on definition 7.97 Partial derivative; gradient ¶
      • depends_on equation 8.4 eq:cpx-derivative ¶
      • proves proof ch:06-complex-analysis@proof-3 ¶
    • 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 ¶ ↺
      • proves proof ch:14-fluid-dynamics@proof-12 ¶
    • proves proof ch:14-fluid-dynamics@proof-31 ¶
  • depends_on theorem 8.24 Residue theorem ¶
    • depends_on corollary 8.15 Deformation of contours ¶
      • depends_on definition 6.17 Simply connected space ¶
        • depends_on definition 6.6 Continuous map ¶
        • depends_on definition 6.15 Path-connected space ¶
      • depends_on theorem 8.12 Cauchy ¶
        • depends_on equation 8.5 eq:cpx-cr ¶
        • depends_on theorem 7.131 Green ¶
        • proves proof ch:06-complex-analysis@proof-7 ¶
      • proves proof ch:06-complex-analysis@proof-9 ¶
    • depends_on definition 8.22 Isolated singularities; residue ¶
      • depends_on lemma 8.11 The fundamental $2\pi\ii$ ¶
        • depends_on equation 8.6 eq:cpx-contour-integral ¶
        • depends_on proposition 8.4 Euler's formula ¶
        • proves proof ch:06-complex-analysis@proof-6 ¶
      • depends_on theorem 8.21 Laurent expansion ¶
        • depends_on corollary 8.15 Deformation of contours ¶ ↺
        • depends_on lemma 8.11 The fundamental $2\pi\ii$ ¶ ↺
        • depends_on theorem 8.16 Cauchy integral formula ¶
        • depends_on theorem 8.20 Taylor expansion ¶
        • proves proof ch:06-complex-analysis@proof-15 ¶
    • depends_on lemma 8.11 The fundamental $2\pi\ii$ ¶ ↺
    • depends_on theorem 8.21 Laurent expansion ¶ ↺
    • proves proof ch:06-complex-analysis@proof-17 ¶
  • proves proof ch:14-fluid-dynamics@proof-32 ¶

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