arXiv subjects

Vittorio Pane

Publications and source records attributed to Vittorio Pane.

3 recordsLinked to original sources

arXiv2026

The IBVP for the Navier-Stokes equations in the half-space in a class of weighted Lebesgue spaces

We study the initial-boundary value problem for the Navier-Stokes equations in the half-space with initial data belonging to a suitable weighted Lebesgue space. More precisely, we consider a weighted Lebesgue space associated with a weight function defined as a product of powers of the distances from finitely many fixed points. This framework was introduced in a previous work by A. P. Di Feola and V. Pane (J. Math. Anal. Appl. 558 (2026), 130390) for the study of the initial-boundary value problem for the Stokes system. The present paper completes that analysis and, at the same time, generalizes to the initial-boundary value problem the results obtained by Maremonti and Pane (J. Math. Fluid Mech. 27 (2025), Art. 2) for the Navier-Stokes Cauchy problem. We prove the existence (local) and uniqueness of a smooth solution and derive $L^q$-estimates, with $q>n$, together with the spatial asymptotic behavior of the velocity field.

math.AP↗

arXiv2025

Weighted estimates for the Stokes semigroup in the half-space

We investigate the initial-boundary value problem for the Stokes system in the half-space, within the framework of weighted Lebesgue spaces. Introducing a new weight function defined via a product of powers of distances from fixed points, we establish existence, uniqueness, and regularity results for strong solutions to the Stokes problem in the half space. Our analysis generalizes previous results for the Stokes system in radial-weighted spaces (Galdi and Maremonti, J. Math. Fluid Mech. 25:7,2023; Maremonti and Pane, J. Math. Fluid Mech. 27:2,2025) and extends the theory to our setting. These results represent a first step toward the analysis of the Navier-Stokes system in weighted spaces, with applications in both half-space and exterior domain configurations.

math.AP↗

arXiv2024

The Navier-Stokes Cauchy problem in a class of weighted function spaces

We consider the Navier-Stokes Cauchy problem with an initial datum in a weighted Lebesgue space. The weight is a radial function increasing at infinity. Our study partially follows the ideas of the paper by G.P. Galdi and P. Maremonti "On the stability of steady-state solutions to the Navier-Stokes equations in the whole space", JMFM, 25 (2023). The authors of the quoted paper consider a spatial study of stability of steady fluid motions. The result hold in 3D and for small data. Here, relatively to the perturbations of the rest state, we generalize the result. We study the nD Navier-Stokes Cauchy problem, n greater than 2. We prove the existence (local) of a unique regular solution. Moreover, the solution enjoys a spatial asymptotic decay whose order of decay is connected to the weight.

math.AP↗