OAI/MathematicalPhysics/DefocusingNLS/Linear/ExpandingSolutionContinuity.lean

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Continuity of bounded actual mild-solution families

The local polynomial Lipschitz estimate is used only along the actual two solutions. Exponential weighting gives a uniform pair contraction, so continuity follows from continuity of the Picard map at a fixed path. No globally Lipschitz extension of the reaction is introduced.

  1. theorem OAI.DefocusingNLS.continuous_fixed_family_of_pair_contraction line 21
  2. theorem OAI.DefocusingNLS.continuous_expandingMild_family line 43
  3. theorem OAI.DefocusingNLS.continuous_expandingMild_bounded_family line 85