Scattering and blowup for L²-supercritical and H²-subcritical biharmonic NLS with potentials

2018/10/16 by Guo, Qing, Wang, Hua, Yao, Xiaohua
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.07104

Abstract

We mainly consider the focusing biharmonic Schrödinger equation with a large radial repulsive potential V(x): \ \beginaligned iu_t+(Δ²+V)u-|u|^p-1u=0, (t,x) ∈ \bfR×\bfR^N, u(0, x)=u₀(x)∈ H²(\bfR^N), \endaligned. If N>8, 1+(8)/(N)N+4, then we firstly prove a global well-posedness and scattering result for the radial data u₀∈ H²(\bf R^N) which satisfies that M(u₀)^{(2-s_c)/(s_c)}E(u₀)‖Q‖^{(2-s_c)/(s_c)}_L²‖ΔQ‖_L².

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