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arXiv · 2601.20294

Norm inflation for quadratic derivative fractional nonlinear Schr\"odinger equations

Toshiki Kondo·Mamoru Okamoto
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Abstract

We consider the Cauchy problem for quadratic derivative fractional nonlinear Schr\"odinger equations on $\mathbb{R}$ or $\mathbb{T}$. We determine the sharp exponents of the fractional derivatives for which the Cauchy problem is well-posed in the Sobolev space. Thanks to the global well-posedness result established by Nakanishi and Wang (2025), we can expand the solution as a sum of iterated terms. By deriving estimates for each iterated term, we establish norm inflation with infinite loss of regularity, which in particular implies ill-posedness.

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Toshiki Kondo, Mamoru Okamoto. 2026-01-28. Norm inflation for quadratic derivative fractional nonlinear Schr\"odinger equations. https://doi.org/10.1007/s00028-026-01223-9

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