2023/09/15 by Mingxuan He, He, Mingxuan, Na Deng +1
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2309.08278
openalex publication_date 2023/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove the local and global well-posedness of the time fractional abstract Schrödinger type evolution equation on the Hilbert space and as an application, we prove the local and global well-posedness of the fractional dispersive equation with static potential under the only assumption that the symbol of P(D) behaves like a polynomial of highest degree m at infinity. In appendix, we also give the Holder regularities and the asymptotic behaviors of the mild solution to the linear time fractional abstract Schrödinger type equation. Because of the lack of the semigroup properties of the solution operators, we employ a strategy of proof based on the spectral theorem of the self-adjoint operators and the asymptotic behaviors of the Mittag-Leffler functions.