Journal article
Dynamics of threshold solutions for energy critical NLW with inverse square potential
Mathematische Zeitschrift, Vol.302(1), pp.353-389
06/23/2022
DOI: 10.1007/s00209-022-03068-7
Abstract
We consider the focusing energy critical NLW with inverse square potential in dimensions d= 3 , 4 , 5. Solutions on the energy surface of the ground state are characterized. We prove that solutions with kinetic energy less than that of the ground state must scatter to zero or belong to the stable/unstable manifold of the ground state. In the latter case they converge to the ground state exponentially in the energy space as t→ ∞ or t→ - ∞. When the kinetic energy is greater than that of the ground state, we show that all solutions with finite mass blow up in finite time in both time directions in d= 3 , 4. In d= 5 , a finite mass solution can either have finite lifespan or lie on the stable/unstable manifolds of the ground state. The proof relies on the detailed spectral analysis of the linearized operator, local invariant manifold theory, and a global Virial analysis.
Details
- Title: Subtitle
- Dynamics of threshold solutions for energy critical NLW with inverse square potential
- Creators
- Kai Yang - Southeast UniversityXiaoyi Zhang
- Resource Type
- Journal article
- Publication Details
- Mathematische Zeitschrift, Vol.302(1), pp.353-389
- DOI
- 10.1007/s00209-022-03068-7
- ISSN
- 0025-5874
- eISSN
- 1432-1823
- Language
- English
- Date published
- 06/23/2022
- Academic Unit
- Mathematics
- Record Identifier
- 9984273657702771
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