WebTIME-DEPENDENT SCHRODINGER-HARTREE EQUATION Hristo Genev So a University St. Kl. Ohridski ... Nonlinear Schr odinger equation, solitary waves, blow-up solutions, variational methods. 903. Web01. dec 2024. · We study stable blow‐up dynamics in the generalized Hartree equation with radial symmetry, which is a Schrödinger‐type equation with a nonlocal, convolution‐type nonlinearity: First, we ...
Energy thresholds of blow‐up for the Hartree equation with a …
WebWe study the generalized Hartree equation, which is a nonlinear Schrödinger-type equation with a nonlocal potential [Formula: see text]. We establish the local well-posedness at the nonconserved critical regularity [Formula: see text] for [Formula: see text], which also includes the energy-supercritical regime [Formula: see text] (thus, … WebWe study the generalized Hartree equation, which is a nonlinear Schrödinger-type equation with a nonlocal potential i u t + Δ u + ( x − b ∗ u p) u p − 2 u = 0, x ∈ ℝ N.We establish the local well-posedness at the nonconserved critical regularity Ḣ s c for s c ≥ 0, which also includes the energy-supercritical regime s c > 1 (thus, complementing the … bhel market value
Stability of standing waves for the fractional Schrödinger–Hartree equation
Web03. apr 2013. · The purpose of this work is to identify a sharp criterion under which energy solutions of L 2 supercritical Hartree equation scatter. From the view of physical point, the criterion is represented in terms of the corresponding Lagrange functional and the virial quantity. This differs from Duyckaers et al. (Math Res Lett 15(6):1233–1250, 2008) … Web02. okt 2024. · In the intercritical setting the criterion produces blow-up solutions with the initial values above the mass-energy threshold. We conclude with examples showing currently known thresholds for global vs. finite time behavior. Subjects: Analysis of PDEs (math.AP) Cite as: arXiv:1910.01085 [math.AP] (or arXiv:1910.01085v1 [math.AP] for … Web15. feb 2024. · Motivated by this problem, we study the scattering versus blow-up dichotomy of the solutions for the focusing L 2-supercritical, nonlinear, fractional Schrödinger equation (1.1). Similar to studies on the classical semi-linear Schrödinger equation (see [5] , [33] , [38] ), we attempt to use the variational method to find a sharp threshold of ... bhella cristy tiktok