Existence of normalized least-energy solutions to the stationary fractional NLS is established on a constrained L2-submanifold, shown to coincide with unconstrained ground states, yielding sharp global/blow-up thresholds and instability by blow-up for the time-dependent equation.
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Normalized ground states for the fractional nonlinear Schr\"{o}dinger equations
Existence of normalized least-energy solutions to the stationary fractional NLS is established on a constrained L2-submanifold, shown to coincide with unconstrained ground states, yielding sharp global/blow-up thresholds and instability by blow-up for the time-dependent equation.