Sharp Threshold of Global Existence and Mass Concentration for the Schrödinger–Hartree Equation with Anisotropic Harmonic Confinement
Min Gong and
Hui Jian
Advances in Mathematical Physics, 2023, vol. 2023, issue 1
Abstract:
This article is concerned with the initial‐value problem of a Schrödinger–Hartree equation in the presence of anisotropic partial/whole harmonic confinement. First, we get a sharp threshold for global existence and finite time blow‐up on the ground state mass in the L2‐critical case. Then, some new cross‐invariant manifolds and variational problems are constructed to study blow‐up versus global well‐posedness criterion in the L2‐critical and L2‐supercritical cases. Finally, we research the mass concentration phenomenon of blow‐up solutions and the dynamics of the L2‐minimal blow‐up solutions in the L2‐critical case. The main ingredients of the proofs are the variational characterisation of the ground state, a suitably refined compactness lemma, and scaling techniques. Our conclusions extend and compensate for some previous results.
Date: 2023
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https://doi.org/10.1155/2023/4316819
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2023:y:2023:i:1:n:4316819
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