definition A.715 Stokes stream function

open in the book · appendices/A-long-proofs.tex:34602 · p. 3140

ground object -- no derivation owed

Rests on

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 ¶
      - 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 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 ¶

Supports

depends_on lemma A.716 The creeping-flow equation for $\psi$ ¶
- 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`	→	eq:ana-nabla-sph-grad	declared	appendices/A-long-proofs.tex:34611
`depends_on`	→	The stream function of a plane flow	declared	appendices/A-long-proofs.tex:34611
`depends_on`	←	The creeping-flow equation for $\psi$	declared	appendices/A-long-proofs.tex:34638