scholarly journals Blow-up and scattering for the 1D NLS with point nonlinearity above the mass–energy threshold

2021 ◽  
pp. 132978
Author(s):  
Alex H. Ardila
Keyword(s):  
Blow Up ◽  
Energy Threshold ◽  
Mass Energy

Well-posedness and blow-up properties for the generalized Hartree equation

2020 ◽  
Vol 17 (04) ◽  
pp. 727-763
Author(s):  
Anudeep Kumar Arora ◽  
Svetlana Roudenko
Keyword(s):  
Finite Time ◽  
Blow Up ◽  
Hartree Equation ◽  
Energy Threshold ◽  
Local Theory ◽  
Positive Energy ◽  
Small Data ◽  
Well Posedness ◽  
Time Behavior ◽  
Mass Energy

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.

Derivation of the photon mass-energy threshold

2005 ◽  
Author(s):  
Riccardo C. Storti ◽  
Todd J. Desiato
Keyword(s):  
Energy Threshold ◽  
Photon Mass ◽  
Mass Energy

scholarly journals Mass-energy threshold dynamics for dipolar quantum gases

2022 ◽  
Vol 20 (1) ◽  
pp. 165-200
Author(s):  
Van Duong Dinh ◽  
Luigi Forcella ◽  
Hichem Hajaiej
Keyword(s):  
Quantum Gases ◽  
Energy Threshold ◽  
Threshold Dynamics ◽  
Mass Energy

Positive solutions for a quasilinear system Via blow up

1993 ◽  
Vol 18 (12) ◽  
pp. 2071-2106
Author(s):  
Philippe Clément ◽  
Raúl Manásevich ◽  
Enzo Mitidieri
Keyword(s):  
Positive Solutions ◽  
Blow Up ◽  
Quasilinear System

: The Blow-Up . Michelangelo Antonioni .

1967 ◽  
Vol 20 (3) ◽  
pp. 28-31
Author(s):  
Max Kozloff
Keyword(s):  
Blow Up ◽  
Michelangelo Antonioni
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