scholarly journals Polyhomogeneous expansions from time symmetric initial data

2017 ◽  
Vol 34 (19) ◽  
pp. 195007 ◽  
Author(s):  
E Gasperín ◽  
J A Valiente Kroon
Keyword(s):  
Initial Data ◽  
Symmetric Initial Data

scholarly journals Dain’s invariant on non-time symmetric initial data sets

2017 ◽  
Vol 34 (12) ◽  
pp. 125013 ◽  
Author(s):  
J A Valiente Kroon ◽  
J L Williams
Keyword(s):  
Initial Data ◽  
Data Sets ◽  
Symmetric Initial Data

scholarly journals GLOBAL REGULARITY FOR A LOGARITHMICALLY SUPERCRITICAL DEFOCUSING NONLINEAR WAVE EQUATION FOR SPHERICALLY SYMMETRIC DATA

2007 ◽  
Vol 04 (02) ◽  
pp. 259-265 ◽  
Author(s):  
TERENCE TAO
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Global Regularity ◽  
Spherically Symmetric ◽  
Supercritical Regime ◽  
Critical Equation ◽  
Critical Regularity ◽  
Spatial Dimensions ◽  
Symmetric Initial Data ◽  
Supercritical Wave Equation

We establish global regularity for the logarithmically energy-supercritical wave equation □u = u5 log (2 + u2) in three spatial dimensions for spherically symmetric initial data, by modifying an argument of Ginibre, Soffer and Velo for the energy-critical equation. This example demonstrates that critical regularity arguments can penetrate very slightly into the supercritical regime.

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