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| title = Uniform decay estimate and the Lorentz invariance of the classical wave equations

...}</math> by Strichartz estimates ([[LbSo1995]]).This is sharp from Lorentz invariance (concentration) considerations.

* [[Gauge]] invariance * [[Lorentz]] symmetry

...as sub-critical, critical, or super-critical with respect to this scaling invariance. ''Example'': In the [[cubic NLS on R3|cubic NLS on R^3]], the energy or < ...t to other symmetries than scaling, such as Galilean invariance or Lorentz invariance.

relies on [[Lorentz invariance]] of the solutions. We consider the reference frame where the solutions dep being this the way the scalar field changes under the effect of a Lorentz transformation <math>\, \Lambda \!</math> and being here <math>\, x_\mu=(t,

...WP has also been obtained in Besov spaces [[Pl2000]], [[Pl-p]] and Fourier-Lorentz spaces [[CaVeVi-p]] at the scaling of <math>L^2\,</math>. This is also conn ** Below <math>L^2\,</math> we have ill-posedness by Gallilean invariance considerations in both the focusing [[KnPoVe2001]] and defocusing [[CtCoTa-

C. Cronstrom, ''A simple and complete Lorentz-invariant gauge condition'', Phys. Lett. B '''90''' (1980), 267-269. J. Ginibre, G. Velo, ''Conformal invariance and time decay for nonlinear wave equations I.'' Ann. Inst. Henri Poncare P