OAI/MathematicalPhysics/DefocusingNLS/Nonlinear/StableGraphSlabGluing.lean

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12 declarations, 0 contain sorry, 0 declared as axioms

Gluing the finite trajectories selected by a stable endpoint sequence

Adjacent closed slabs agree at their endpoints. Their locally finite cover therefore gives one continuous trajectory, with the same geometric decay between the discrete times. This is a supporting construction; its inputs are actual finite trajectories and their proved endpoint identities.

  1. def OAI.DefocusingNLS.equalSlabInterval line 20
  2. theorem OAI.DefocusingNLS.equalSlabInterval_floor line 23
  3. theorem OAI.DefocusingNLS.equalSlabInterval_cover line 29
  4. theorem OAI.DefocusingNLS.equalSlabInterval_locallyFinite line 39
  5. def OAI.DefocusingNLS.equalSlabPiece line 53
  6. theorem OAI.DefocusingNLS.continuous_equalSlabPiece line 57
  7. theorem OAI.DefocusingNLS.equalSlabPiece_compatible line 62
  8. def OAI.DefocusingNLS.gluedSlabPath line 92
  9. theorem OAI.DefocusingNLS.gluedSlabPath_eq line 103
  10. theorem OAI.DefocusingNLS.gluedSlabPath_at line 112
  11. theorem OAI.DefocusingNLS.continuousOn_gluedSlabPath line 121
  12. theorem OAI.DefocusingNLS.gluedSlabPath_tendsto_zero line 134