Theorems · Theorem · ordinary differential equations

isIntegralCurve_const

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {v : ℝ → E → E} {x : E},
  (∀ (t : ℝ), v t x = 0) → IsIntegralCurve (fun x_1 => x) v

If the vector field v vanishes at x₀ for all times, then the constant curve at x₀ is a global integral curve of v.

Defined in

Mathlib.Analysis.ODE.Transform

Cited by

0 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace