lemma A.716 The creeping-flow equation for $\psi$

open in the book · appendices/A-long-proofs.tex:34626 · p. 3140

Rests on

depends_on definition A.715 Stokes stream function ¶
- depends_on equation 7.131 eq:ana-nabla-sph-grad ¶
- depends_on example 31.15 The stream function of a plane flow ¶
  - 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 ¶
      - proves proof ch:14-fluid-dynamics@proof-5 ¶
    - proves proof ch:14-fluid-dynamics@proof-6 ¶
  - 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 7.99 Differentiability at a point ¶
      - depends_on definition 7.102 Differential of a function ¶
      - 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 theorem 7.131 Green ¶
      - proves proof ch:05-real-analysis@proof-78 ¶
    - proves proof ch:05-real-analysis@proof-80 ¶
depends_on definition 31.43 Creeping flow ¶
- depends_on equation 31.42 eq:fluid-reynolds-number ¶
- 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 ¶
    - depends_on definition 31.21 Ideal fluid ¶
      - depends_on definition 31.1 Fluid ¶ ↺
    - 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-18 ¶
proves proof app:A-long-proofs@proof-419 ¶

Supports

depends_on lemma A.717 The radial solution ¶
- depends_on theorem A.718 Stokes' drag law with its coefficient ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Stokes stream function	declared	appendices/A-long-proofs.tex:34638
`depends_on`	→	Creeping flow	declared	appendices/A-long-proofs.tex:34638
`depends_on`	←	The radial solution	declared	appendices/A-long-proofs.tex:34703
`proves`	←	app:A-long-proofs@proof-419	declared	appendices/A-long-proofs.tex:34641