Threshold dynamics for the 3d radial NLS with combined nonlinearity

2023/05/22 by Ardila, Alex H., Murphy, Jason, Zheng, Jiqiang
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.13531

Abstract

We consider the nonlinear Schrödinger equation with focusing quintic and defocusing cubic nonlinearity in three space dimensions: (i∂_t+Δ)u = |u|² u - |u|⁴ u. In [18, 23], the authors classified the dynamics of solutions under the energy constraint E(u)< E^c(W), where W is the quintic NLS ground state and E^c is the quintic NLS energy. In this work we classify the dynamics of H¹ solutions at the threshold E(u)=E^c(W).

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