We prove space–time decay estimates of suitable weak solutions to the Navier– Stokes Cauchy problem, corresponding to a given asymptotic behavior of the initial data of the same order of decay. We use two main tools. The first is a result obtained in [7] for the behavior of the solution in a neighborhood of t = 0 in the  -norm, which enables us to furnish a representation formula for a suitable weak solution. The second is the asymptotic behavior of ∥u(t)∥L2(R3\BR) for R → ∞. Following Leray’s point of view, roughly speaking our result proves that a possible space–time turbulence does not perturb the asymptotic spatial behavior of the initial data of a suitable weak solution.
On the spatial asymptotic decay of a suitable weak solution to the Navier–Stokes Cauchy problem
CRISPO, Francesca;MAREMONTI, Paolo
2016
Abstract
We prove space–time decay estimates of suitable weak solutions to the Navier– Stokes Cauchy problem, corresponding to a given asymptotic behavior of the initial data of the same order of decay. We use two main tools. The first is a result obtained in [7] for the behavior of the solution in a neighborhood of t = 0 in the  -norm, which enables us to furnish a representation formula for a suitable weak solution. The second is the asymptotic behavior of ∥u(t)∥L2(R3\BR) for R → ∞. Following Leray’s point of view, roughly speaking our result proves that a possible space–time turbulence does not perturb the asymptotic spatial behavior of the initial data of a suitable weak solution.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
