arXiv subjects

Carlo Romano Grisanti

Publications and source records attributed to Carlo Romano Grisanti.

5 recordsLinked to original sources

arXiv2025

Estimates of a possible gap related to the energy equality for a class of non-Newtonian fluids

The paper is concerned with the 3D-initial value problem for power-law fluids with shear dependent viscosity in a spatially periodic domain. The goal is the construction of a weak solution enjoying an energy equality. The results hold assuming an initial data $v_0\in J^2(Ω)$ and for $p\in \left(\frac 95,2\right)$. It is interesting to observe that the result is in complete agreement with the one known for the Navier-Stokes equations. Further, in both cases, the additional dissipation, which measures the possible gap with the classical energy equality, is only expressed in terms of energy quantities.

math.AP↗

arXiv2022

Navier-Stokes equations: a new estimate of a possible gap related to the energy equality of a suitable weak solution

The paper is concerned with the IBVP of the Navier-Stokes equations. The result of the paper is in the wake of analogous results obtained by the authors in previous articles [4, 5]. The goal is to estimaste the possible gap between the energy equality and the energy inequality deduced for a weak solution.

math.AP↗

arXiv2020

Navier-Stokes equations: an analysis of a possible gap to achieve the energy equality

The paper is concerned with the IBVP of the Navier-Stokes equations. The goal is the attempt to construct a weak solution enjoying an energy equality. This result is a natural continuation and improvement of the one obtained by the same authors in [2].

math.AP↗

arXiv2018

Singular p-Laplacian parabolic system in exterior domains: higher regularity of solutions and related properties of extinction and asymptotic behavior in time

We consider the IBVP in exterior domains for the p-Laplacian parabolic system. We prove regularity up to the boundary, extinction properties for p \in ( 2n/(n+2) , 2n/(n+1) ) and exponential decay for p= 2n/(n+1) .

math.AP↗

arXiv2017

The Caccioppoli Ultrafunctions

Ultrafunctions are a particular class of functions defined on a hyperreal field $\mathbb{R}^{\ast}\supset\mathbb{R}$. They have been introduced and studied in some previous works. In this paper we introduce a particular space of ultrafunctions which has special properties, especially in term of localization of functions together with their derivatives. An appropriate notion of integral is then introduced which allows to extend in a consistent way the integration by parts formula, the Gauss theorem and the notion of perimeter. This new space we introduce, seems suitable for applications to PDE's and Calculus of Variations. This fact will be illustrated by a simple, but meaningful example.

math.AP↗