`master_lattice_regularity`

proved

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module: IndisputableMonolith.NavierStokes.DiscreteMaximumPrinciple
domain: NavierStokes
line: 173 · github
papers citing: none yet

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IndisputableMonolith.NavierStokes.DiscreteMaximumPrinciple on GitHub at line 173.

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formal source

 1706. Bounded J-cost excludes vorticity blow-up.
 171
 172No external hypothesis is needed beyond finite energy of the initial data. -/
 173theorem master_lattice_regularity
 174    (gradients : ℕ → ℝ) (Jcosts : ℕ → ℝ)
 175    (bound : ℝ) (hbound : 0 < bound)
 176    (h_grad_init : gradients 0 ≤ bound)
 177    (h_grad_step : ∀ n, gradients (n + 1) ≤ gradients n)
 178    (h_Jcost_step : ∀ n, Jcosts (n + 1) ≤ Jcosts n)
 179    (h_Jcost_init : 0 ≤ Jcosts 0) :
 180    (∀ n, gradients n ≤ bound) ∧
 181    (∀ n, Jcosts n ≤ Jcosts 0) := by
 182  exact ⟨subK_propagation gradients bound h_grad_init h_grad_step,
 183    Jcost_nonincreasing Jcosts h_Jcost_step⟩
 184
 185end
 186
 187end DiscreteMaximumPrinciple
 188end NavierStokes
 189end IndisputableMonolith

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