scholarly journals Strichartz estimates with loss of derivatives under a weak dispersion property for the wave operator

2019 ◽  
Vol 11 (1) ◽  
pp. 59-78
Author(s):  
Valentin Samoyeau
Keyword(s):  
Wave Operator ◽  
Strichartz Estimates ◽  
Dispersion Property ◽  
Loss Of Derivatives

scholarly journals Dispersive estimates with loss of derivatives via the heat semigroup and the wave operator

2017 ◽  
pp. 969-1029
Author(s):  
Frédéric Bernicot ◽  
Valentin Samoyeau
Keyword(s):  
Wave Operator ◽  
Heat Semigroup ◽  
Loss Of Derivatives

scholarly journals Strichartz estimates and local existence for the gravity–capillary waves with non-Lipschitz initial velocity

2016 ◽  
Vol 261 (1) ◽  
pp. 396-438 ◽  
Author(s):  
Thibault de Poyferré ◽  
Quang-Huy Nguyen
Keyword(s):  
Initial Velocity ◽  
Local Existence ◽  
Capillary Waves ◽  
Strichartz Estimates

scholarly journals Strichartz Estimates and Fourier Restriction Theorems on the Heisenberg Group

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Hajer Bahouri ◽  
Davide Barilari ◽  
Isabelle Gallagher
Keyword(s):  
Heisenberg Group ◽  
Strichartz Estimates ◽  
Fourier Restriction ◽  
Restriction Theorems

scholarly journals QUANTUM SINGULARITIES IN STATIC SPACETIMES

2011 ◽  
Vol 20 (05) ◽  
pp. 729-743 ◽  
Author(s):  
JOÃO PAULO M. PITELLI ◽  
PATRICIO S. LETELIER
Keyword(s):  
Quantum Mechanics ◽  
Wave Operator ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Mathematical Framework ◽  
Physical Content ◽  
Dirac Equations ◽  
Quantum Particles ◽  
Klein Gordon ◽  
Quantum Singularities

We review the mathematical framework necessary to understand the physical content of quantum singularities in static spacetimes. We present many examples of classical singular spacetimes and study their singularities by using wave packets satisfying Klein–Gordon and Dirac equations. We show that in many cases the classical singularities are excluded when tested by quantum particles but unfortunately there are other cases where the singularities remain from the quantum mechanical point of view. When it is possible we also find, for spacetimes where quantum mechanics does not exclude the singularities, the boundary conditions necessary to turn the spatial portion of the wave operator to be self-adjoint and emphasize their importance to the interpretation of quantum singularities.

scholarly journals On global Strichartz estimates for non-trapping metrics

2008 ◽  
Vol 254 (6) ◽  
pp. 1661-1682 ◽  
Author(s):  
Jean-Marc Bouclet ◽  
Nikolay Tzvetkov
Keyword(s):  
Strichartz Estimates
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