Strong Navier–Stokes solutions on a closed time interval #
The class records the C_tH¹ ∩ L²_tH² regularity, L² time derivative,
solenoidal slices, and unregularized equation of prop:lps-local-strong.
def
ESS.IsLpsStrongSolution
(t₀ T : ℝ)
(u : CKN.Foundation.Parabolic.ParabolicPoint → CKN.Foundation.Parabolic.Vec3)
(Du : CKN.Foundation.Parabolic.ParabolicPoint → Fin 3 → CKN.Foundation.Parabolic.Vec3)
(p : CKN.Foundation.Parabolic.ParabolicPoint → ℝ)
:
A strong solenoidal solution on [t₀,T], in the class of
prop:lps-local-strong. Spatial derivatives use Du z i j = ∂ⱼuᵢ and
D2u z i j k = ∂ₖ∂ⱼuᵢ. Continuity into H¹ is expressed through the
L² distance of the velocity and its specified gradient.
Equations
- One or more equations did not get rendered due to their size.