For kinetic wave equations from quasilinear Schrödinger models, local well-posedness in weighted L∞ spaces holds exactly when the derivative-loss parameter β ≤ 1/4, and fails for β > 1/4.
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On the ill-posedness of kinetic wave equations
For kinetic wave equations from quasilinear Schrödinger models, local well-posedness in weighted L∞ spaces holds exactly when the derivative-loss parameter β ≤ 1/4, and fails for β > 1/4.