For quadratic derivative fractional NLS, the Cauchy problem is ill-posed in Sobolev spaces below sharp fractional derivative exponents due to norm inflation with infinite loss of regularity.
Mizuhara,The initial value problem for third and fourth order dispersive equations in one space dimension, Funkcial
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
fields
math.AP 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Norm inflation for quadratic derivative fractional nonlinear Schr\"odinger equations
For quadratic derivative fractional NLS, the Cauchy problem is ill-posed in Sobolev spaces below sharp fractional derivative exponents due to norm inflation with infinite loss of regularity.