Phase space analysis of the Hermite semigroup and applications to nonlinear global well-posedness

DG Bhimani, R Manna, F Nicola, S Thangavelu… - Advances in …, 2021 - Elsevier
We study the Hermite operator H=− Δ+| x| 2 in R d and its fractional powers H β, β> 0 in
phase space. Namely, we represent functions f via the so-called short-time Fourier, alias …

[PDF][PDF] Global well-posedness for Klein-Gordon-Hartree and fractional Hartree equations on modulation spaces

D Bhimani - 2021 - digital.library.txstate.edu
We study the Cauchy problems for the Klein-Gordon (HNLKG), wave (HNLW), and
Schrodinger (HNLS) equations with cubic convolution (of Hartree type) nonlinearity. Some …

On the existence of global solutions of the Hartree equation for initial data in the modulation space Mp, q (R)

R Manna - Journal of Differential Equations, 2022 - Elsevier
In this paper, we study the Cauchy problem for Hartree type equation iu t+ uxx=[K⁎| u| 2] u,
with Cauchy data in modulation spaces M p, q (R). We establish global well-posedness …