Research proof index

The preimage of m under succSuccAbove i j hij given that m is not equal to i or j. -/ def predPredAbove (i j : Fin (n + 1 + 1)) (hij : i ≠ j) (m : Fin (n + 1 + 1)) (hm : m ≠ i ∧ m ≠ j) : Fin n := if h1 : m.1 < i.1 ∧ m.1 < j.1 then ⟨m, by grind⟩ else if h2 : m.1 - 1 < i.1 ∧ j.1 ≤ m.1 then ⟨m - 1, by grind⟩ else if h3 : i.1 - 1 ≤ m.1 ∧ m.1 < j.1 t...

The conservative and convective Cauchy momentum equations are equivalent when the classical continuity equation holds. The differentiability assumptions are exactly the product-rule assumptions used to rewrite partial_t (rho u) and matrixDiv (rho u ⊗ u).

The conservative and convective Euler forms are equivalent when the fields are differentiable enough for the product rules.

The matrix divergence of rho u ⊗ u split into continuity and convective parts.

The conservative momentum transport terms equal mass density times material acceleration plus the continuity residual times velocity.

Product rule for one spatial derivative of one component of rho u ⊗ u.