Global well-posedness for fractional Hartree equation on modulation spaces and Fourier algebra

Abstract

We study the Cauchy problem for fractional Schrödinger equation with cubic convolution nonlinearity (i∂ t u − (−∆) α 2 u ± (K * |u| 2 )u = 0) with Cauchy data in the mod- γ)) when α = 2, d ≥ 1, and with radial Cauchy data when d ≥ 2, 2d 2d−1 < α < 2. Similar results are proven in Fourier2010 Mathematics Subject Classification. 35Q55, 42B35 (primary), 35A01 (secondary).

Human granulocytic anaplasmosis in a Single University Hospital in the Republic of Korea

“…The following is an analog of the above proposition for modulation spaces. Lemma 2.5 (Proposition 3.2 of [1]). Let 0 < γ < d, 1 < p 1 < p 2 < ∞, 1 ≤ q ≤ ∞, and s ≥ 0.…”

Energy criteria of global existence for a class of Hartree equations with Coulomb potential

“…The dynamics of blow-up solutions was investigated in [5,20,22,28,29]. In [2,12,21], they showed the sharp criteria for blow-up and scattering in H 1 (R n ). Huang, Zhang, Chen [16] and Tian, Yang, Zhou [25] showed the sharp criteria of global existence for the Hartree equation with subcritical perturbations.…”

Energy thresholds of blow‐up for the Hartree equation with a focusing subcritical perturbation

“…On the other hand, by removing the power‐type nonlinearity , one recovers the nonlinear Hartree equation, and there are numerous results for the Hartree equation; see Refs. 13–15 for the sharp criteria for blow‐up and scattering in H 1 ; see Refs. 16–18 for the dynamics of blow‐up solutions in L 2 and ; and Refs.…”