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- Title
Sharp Threshold of Global Existence and Mass Concentration for the Schrödinger–Hartree Equation with Anisotropic Harmonic Confinement.
- Authors
Gong, Min; Jian, Hui
- 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 L 2 -critical case. Then, some new cross-invariant manifolds and variational problems are constructed to study blow-up versus global well-posedness criterion in the L 2 -critical and L 2 -supercritical cases. Finally, we research the mass concentration phenomenon of blow-up solutions and the dynamics of the L 2 -minimal blow-up solutions in the L 2 -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.
- Subjects
EQUATIONS; BLOWING up (Algebraic geometry); MASS transfer
- Publication
Advances in Mathematical Physics, 2023, p1
- ISSN
1687-9120
- Publication type
Article
- DOI
10.1155/2023/4316819