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Angelica Pia Di Feola

Publications and source records attributed to Angelica Pia Di Feola.

5 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↗
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↗