An all-orders joint-flow bootstrap from regularity of the spatial jet.

def AVenhance.Infra.Flow.JointSmoothBootstrap.flowTimeVelocityN (b : ℝ → Homogenization.Vec 2 → Homogenization.Vec 2) (X : ℝ → Homogenization.Vec 2 → ℝ → Homogenization.Vec 2) (p : ℝ × Homogenization.Vec 2 × ℝ) : Homogenization.Vec 2

Observation-time velocity in the arbitrary-order joint smoothness bootstrap.

Equations

• AVenhance.Infra.Flow.JointSmoothBootstrap.flowTimeVelocityN b X p = AVenhance.Infra.Flow.JointC1.flowTimeVelocity b X p

noncomputable def AVenhance.Infra.Flow.JointSmoothBootstrap.flowSpatialJacobianN (X : ℝ → Homogenization.Vec 2 → ℝ → Homogenization.Vec 2) (p : ℝ × Homogenization.Vec 2 × ℝ) : Homogenization.Vec 2 →L[ℝ] Homogenization.Vec 2

Spatial Jacobian in the arbitrary-order joint smoothness bootstrap.

Equations

• AVenhance.Infra.Flow.JointSmoothBootstrap.flowSpatialJacobianN X p = AVenhance.Infra.Flow.JointC1.flowSpatialDerivativeAt X p

noncomputable def AVenhance.Infra.Flow.JointSmoothBootstrap.flowStartVelocityN (b : ℝ → Homogenization.Vec 2 → Homogenization.Vec 2) (X : ℝ → Homogenization.Vec 2 → ℝ → Homogenization.Vec 2) (p : ℝ × Homogenization.Vec 2 × ℝ) : Homogenization.Vec 2

Starting-time velocity in the arbitrary-order joint smoothness bootstrap.

Equations

• AVenhance.Infra.Flow.JointSmoothBootstrap.flowStartVelocityN b X p = AVenhance.Infra.Flow.JointC1.flowStartVelocity b X p

noncomputable def AVenhance.Infra.Flow.JointSmoothBootstrap.flowStartCLMN (b : ℝ → Homogenization.Vec 2 → Homogenization.Vec 2) (X : ℝ → Homogenization.Vec 2 → ℝ → Homogenization.Vec 2) (p : ℝ × Homogenization.Vec 2 × ℝ) : ℝ →L[ℝ] Homogenization.Vec 2

Starting-time differential in the arbitrary-order joint smoothness bootstrap.

Equations

• AVenhance.Infra.Flow.JointSmoothBootstrap.flowStartCLMN b X p = AVenhance.Infra.Flow.JointC1.flowStartDerivativeCLM b X p

noncomputable def AVenhance.Infra.Flow.JointSmoothBootstrap.flowParameterDerivativeN (b : ℝ → Homogenization.Vec 2 → Homogenization.Vec 2) (X : ℝ → Homogenization.Vec 2 → ℝ → Homogenization.Vec 2) (p : ℝ × Homogenization.Vec 2 × ℝ) : Homogenization.Vec 2 × ℝ →L[ℝ] Homogenization.Vec 2

Position and starting-time differential in the arbitrary-order joint smoothness bootstrap.

Equations

• AVenhance.Infra.Flow.JointSmoothBootstrap.flowParameterDerivativeN b X p = AVenhance.Infra.Flow.JointC1.flowPairDerivativeAt b X p

noncomputable def AVenhance.Infra.Flow.JointSmoothBootstrap.flowJointDerivativeN (b : ℝ → Homogenization.Vec 2 → Homogenization.Vec 2) (X : ℝ → Homogenization.Vec 2 → ℝ → Homogenization.Vec 2) (p : ℝ × Homogenization.Vec 2 × ℝ) : ℝ × Homogenization.Vec 2 × ℝ →L[ℝ] Homogenization.Vec 2

Full joint differential in the arbitrary-order joint smoothness bootstrap.

Equations

• AVenhance.Infra.Flow.JointSmoothBootstrap.flowJointDerivativeN b X p = AVenhance.Infra.Flow.JointC1.flowJointDerivativeAt b X p