This analysis demonstrates blow-up criteria for solutions to the fractional nonlinear Schrödinger equation, highlighting implications for cylindrically symmetric situations.
In this paper, we consider blow-up of solutions to the Cauchy problem for the following fractional Nonlinear Schrödinger Equation (NLS), {equation*} i \, ∂_t u=(-Δ)^s u-|u|2 σ u in \,\, R × R^N, {equation*} where N ≥ 2 , 1/2 < s < 1 , and 0 < σ < 2s/(N-2s) . In the mass critical and supercritical cases, we establish a criterion for blow-up of solutions to the problem for cylindrically symmetric data. The results extend the known ones with respect to blow-up of solutions to the problem for radially symmetric data.
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Gou et al. (2025) studied this question.
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