OAI/MathematicalPhysics/NavierStokes/ForcedComputation/Scalar/TorusHeatKernelEquation.lean

GitHub source file

10 declarations, 0 contain sorry, 0 declared as axioms

The Gaussian lattice kernel satisfies the coordinate heat equation. Fourier products keep the two first and second spatial derivatives explicit.

  1. def OAI.ForcedComputation.VelocityDetector.torusHeatFourierProduct line 13
  2. theorem OAI.ForcedComputation.VelocityDetector.torusHeatFourierProduct_time line 16
  3. theorem OAI.ForcedComputation.VelocityDetector.moment_plane_deriv line 31
  4. theorem OAI.ForcedComputation.VelocityDetector.torusHeatFourierProduct_spatialD_zero line 42
  5. theorem OAI.ForcedComputation.VelocityDetector.torusHeatFourierProduct_spatialD_one line 59
  6. theorem OAI.ForcedComputation.VelocityDetector.torusHeatKernel_eq_fourierProduct line 76
  7. theorem OAI.ForcedComputation.VelocityDetector.torusHeatKernel_laplacian line 82
  8. theorem OAI.ForcedComputation.VelocityDetector.torusHeatFourierProduct_exp_smooth line 96
  9. theorem OAI.ForcedComputation.VelocityDetector.torusHeatKernel_laplacian_exp_smooth line 107
  10. theorem OAI.ForcedComputation.VelocityDetector.torusHeatKernel_equation line 115