2014/12/18 by Félix Ali Mehmeti, F. Ali Mehmeti, Mehmeti, F. Ali +3 · 2 citations
Mathematics · #35B30 #35B40 #35Q41 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Numerical methods in inverse problems #Primary 41A80 #Secondary 41A60 #math.AP #msc:35B30 #msc:35B40 #msc:35Q41 #msc:41A60 #msc:41A80
paper · pdf · doi:10.48550/arxiv.1412.5789
This paper is part I of a series of two articles. The title of the second part is: "Explicit error estimates for the stationary phase method II: Interaction of amplitude singularities with stationary points"
arxiv created 2014/12/18 · openalex publication_date 2014/12/18 · arxiv updated 2014/12/19 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider a version of the stationary phase method in one dimension of A. Erdélyi, allowing the phase to have stationary points of non-integer order and the amplitude to have integrable singularities. We provide a complete proof and we improve the remainder estimates in the case of regular amplitude. Then we are interested in the time-asymptotic behaviour of the solution of the free Schrödinger equation on the line, where the Fourier transform of the initial data is compactly supported and has a singularity. Applying the above mentioned method, we obtain asymptotic expansions with respect to time in certain space-time cones, where the coefficients of the remainders are uniformly bounded. These results show the influence of the singularity on the decay.