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Blow-up and scattering for the 1D NLS with point nonlinearity above the mass-energy threshold (2106.09139v1)
Published 16 Jun 2021 in math.AP
Abstract: In this paper, we study the nonlinear Schr\"odinger equation with focusing point nonlinearity in dimension one. First, we establish a scattering criterion for the equation based on Kenig-Merle's compactness-rigidity argument. Then we prove the energy scattering below and above the mass-energy threshold. We also describe the dynamics of solutions with data at the ground state threshold. Finally, we prove a blow-up criteria for the equation with initial data with arbitrarily large energy.