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The class of Divergence-free symmetric tensors is ubiquitous in Continuum Mechanics. We show its invariance under projective transformations of the independent variables. This action, which preserves the positiveness, extends Sophus Lies group analysis of Newtonian dynamics.When applied to models of gas dynamics --~such as Euler system or Boltzmann equation,~-- in combination with Compensated Integrability, this yields new dispersive estimates. The most accurate one is obtained for mono-atomic gases. Then the space-time integral of $trho^frac1d p$ is bounded in terms of the total mass and moment of inertia alone.
Divergence-free symmetric tensors seem ubiquitous in Mathematical Physics. We show that this structure occurs in models that are described by the so-called second variational principle, where the argument of the Lagrangian is a closed differential fo
We present sharp conditions on divergence-free drifts in Lebesgue spaces for the passive scalar advection-diffusion equation [ partial_t theta - Delta theta + b cdot abla theta = 0 ] to satisfy local boundedness, a single-scale Harnack inequality,
We develop the techniques of cite{KS1} and cite{ES1} in order to derive dispersive estimates for a matrix Hamiltonian equation defined by linearizing about a minimal mass soliton solution of a saturated, focussing nonlinear Schrodinger equation {c} i
We investigate the dispersive properties of solutions to the Schrodinger equation with a weakly decaying radial potential on cones. If the potential has sufficient polynomial decay at infinity, then we show that the Schrodinger flow on each eigenspac
We consider the motion of a finite though large number of particles in the whole space R n. Particles move freely until they experience pairwise collisions. We use our recent theory of divergence-controlled positive symmetric tensors in order to esta