Endpoint Strichartz Estimates for Charge Transfer Hamiltonians

2015/07/14 by Qingquan Deng, Avy Soffer, Deng, Qingquan +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1507.03870

openalex publication_date 2015/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the optimal endpoint Strichartz estimates for Schrödinger equation with charge transfer potentials and a general source term in ℝⁿ for n≥3. The proof is based on using the projection on the scattering states defined implicitly in Rodnianski, Schlag and Soffer \citeRSS1, and asymptotic completeness for such systems. The method works as well in the matrix non-selfadjoint case.

Citations

• Spectral properties of Schrödinger operators and time-decay of the wave functions
• Asymptotic stability of N-soliton states of NLS
• Solitary Wave Dynamics in an External Potential
• Time decay for solutions of Schr�dinger equations with rough and time-dependent potentials

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