We prove spacetime weighted-L2 estimates for the SchrÃ¶dinger and wave equation with an inverse-square potential. We then deduce Strichartz estimates for these equations.

There have been many studies of the well-posedness and decay of scalar fields in a given space-time whose metric satisfies the Einstein equations of general relativity, both as a precursor to theâ€¦ (More)

We present a new variational formulation for relativistic dynamics of isotropic hyperelastic solids. We introduce the shear strain tensor and study the geometry of characteristics in the cotangentâ€¦ (More)

The Cauchy problem is revisited for the so-called relativistic Vlasovâ€“Poisson system in the attractive case, originally studied by Glassey and Schaeffer in 1985. It is proved that a unique globalâ€¦ (More)

We obtain global space-time weighted-L (Morawetz) and L (Strichartz) estimates for a massless chargeless spherically symmetric scalar field propagating on a super-extremal (overcharged)â€¦ (More)

Quasilinear hyperbolic systems have a special place in the theory of partial differential equations since most of the PDEs arising in continuum physics are of this form. Well-known examples are theâ€¦ (More)

We prove spacetime weighted-L2 estimates for the SchrÃ¶dinger and wave equation with an inverse-square potential. We then deduce Strichartz estimates for these equations.

Quasilinear hyperbolic systems have a special place in the theory of partial differential equations since most of the PDEs arising in continuum physics are of this form. Well-known examples are theâ€¦ (More)

We prove spacetime weighted-L2 estimates for the SchrÃ¶dinger and wave equation with an inverse-square potential. We then deduce Strichartz estimates for these equations.