Burgers dynamics for Poisson point process initial conditions of the Weibull class (opens in new tab)

We derive the statistical properties of one-dimensional Burgers dynamics with stochastic initial conditions for the velocity potential defined by a Poisson point process whose intensity follows a power law with exponent . This choice realizes a broad and analytically tractable family of strongly non-Gaussian initial states, relevant as limiting cases for problems ranging from turbulence phenomenology to simplified models of structure formation in cosmology. Working in the inviscid limit and e...