Derivation of the photon mass-energy threshold

2005 ◽  
Author(s):  
Riccardo C. Storti ◽  
Todd J. Desiato
2020 ◽  
Vol 17 (04) ◽  
pp. 727-763
Author(s):  
Anudeep Kumar Arora ◽  
Svetlana Roudenko

We 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, complementing the work in [A. K. Arora and S. Roudenko, Global behavior of solutions to the focusing generalized Hartree equation, Michigan Math J., forthcoming], where we obtained the [Formula: see text] well-posedness in the intercritical regime together with classification of solutions under the mass–energy threshold). We next extend the local theory to global: for small data we obtain global in time existence and for initial data with positive energy and certain size of variance we show the finite time blow-up (blow-up criterion). 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.


2003 ◽  
Vol 68 (5) ◽  
pp. 757-764 ◽  
Author(s):  
Bassam Z. Shakhreet ◽  
C.S. Chong ◽  
T. Bandyopadhyay ◽  
D.A. Bradley ◽  
A.A. Tajuddin ◽  
...  

2022 ◽  
Vol 20 (1) ◽  
pp. 165-200
Author(s):  
Van Duong Dinh ◽  
Luigi Forcella ◽  
Hichem Hajaiej

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