scholarly journals Finite-time blowup for a Schrödinger equation with nonlinear source term

2019 ◽  
Vol 39 (2) ◽  
pp. 1171-1183 ◽  
Author(s):  
Thierry Cazenave ◽  
◽  
Yvan Martel ◽  
Lifeng Zhao ◽  
◽  
...  
Keyword(s):  
Schrödinger Equation ◽  
Finite Time ◽  
Schrodinger Equation ◽  
Source Term ◽  
Nonlinear Source ◽  
Finite Time Blowup ◽  
Time Blowup

scholarly journals Blowup of Solutions to the Compressible Euler-Poisson and Ideal MHD Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Wenming Hu
Keyword(s):  
Finite Time ◽  
Euler System ◽  
Time Dependent ◽  
Poisson System ◽  
Blowup Of Solutions ◽  
Finite Time Blowup ◽  
Ideal Mhd ◽  
Compressible Euler ◽  
Time Blowup

In the present paper, we study the blowup of the solutions to the full compressible Euler system and pressureless Euler-Poisson system with time-dependent damping. By some delicate analysis, some Riccati-type equations are achieved, and then, the finite time blowup results can be derived.

ON ONE BLOW UP POINT SOLUTIONS TO THE CRITICAL NONLINEAR SCHRÖDINGER EQUATION

2005 ◽  
Vol 02 (04) ◽  
pp. 919-962 ◽  
Author(s):  
FRANK MERLE ◽  
PIERRE RAPHAEL
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Ground State ◽  
Finite Time ◽  
Schrodinger Equation ◽  
Blow Up ◽  
Nonlinear Schrodinger Equation ◽  
Specific Class ◽  
Nonlinear Schrödinger ◽  
Existence And Stability

We consider the L2 critical nonlinear Schrödinger equation [Formula: see text] in the energy space H1. In the series of papers [11–15,18], we studied finite time blow up solutions for which lim t↑T < + ∞ |∇ u(t)|L2 = + ∞ and proved classification results of the blow up dynamics for the specific class of small super critical L2 mass initial data. We extend these results here to a wider class of finite time blow up solutions corresponding to the ones which accumulate at one point exactly the ground state mass. In particular, we prove the existence and stability of large L2 mass log-log type solutions which are believed to describe the generic blow up dynamics.

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