DYNAMICS OF THE COMBINED NONLINEAR SCHRÖDINGER EQUATION WITH INVERSE-SQUARE POTENTIAL

作     者：Ma, Zuyu Song, Yilin Zheng, Jiqiang 

作者机构：The Graduate School of China Academy of Engineering Physics Beijing100088 China Institute of Applied Physics and Computational Mathematics Beijing100088 China National Key Laboratory of Computational Physics Beijing100088 China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2024年

核心收录：

主　　题：Ground state 

摘      要：We consider the long-time dynamics of focusing energy-critical Schrödinger equation perturbed by the H1/2 -critical nonlinearity and with inverse-square potential(CNLSa) in dimensions d ∈ {3, 4, 5} (Equation Presented), (t, x) ∈ R × Rd, (CNLSa) where La = −∆ + a|x|−2 and the energy is below and equal to the threshold ma, which is given by the ground state Wa satisfying (Equation Presented) Wa. When the energy is below the threshold, we utilize the concentration-compactness argument as well as the variatonal analysis to characterize the scattering and blow-up region. When the energy is equal to the threshold, we use the modulation analysis associated to the equation (CNLSa) to classify the dynamics of Ha1-solution. In both regimes of scattering results, we do not need the radial assumption in d = 4, 5. Our result generalize the scattering results of [31–33] and [3] in the setting of standard combined NLS. © 2024, CC BY.