Analyticity and infinite breakdown of regularity in mass-subcritical Hartree scattering

2021/03/15 by Gyu Eun Lee, Lee, Gyu Eun
Mathematics · Physics and Astronomy · #35B30 #35B40 (Secondary) #35Q55 (Primary) 35Q40 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35B30 #msc:35B40 #msc:35Q40 #msc:35Q55

paper · pdf · doi:10.48550/arxiv.2103.08770

arxiv created 2021/03/15 · arxiv updated 2021/03/17

Abstract

We study the asymptotic behavior of solutions to the defocusing mass-subcritical Hartree NLS iu_t + Δu = F(u) = (|x|^-γ*|u|²)u on ℝ^d, d≥ 2, (4)/(3) < γ< 2. We show that the scattering problem associated to this equation is analytically well-posed in the weighted spaces Σ= H¹\capFH¹ and FH¹. Furthermore, we show that the same problem fails to be analytically well-posed for data in L². This constitutes an infinite loss of regularity between the scattering problems in weighted spaces and in L². This further develops an earlier investigation initiated by the author in which a finite breakdown of regularity was proved for the L² scattering problem for the mass-subcritical NLS with power nonlinearity F(u) = |u|^pu.

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