arXiv subjects

Cilon F. Perusato

Publications and source records attributed to Cilon F. Perusato.

7 recordsLinked to original sources

arXiv2026

On the Role of the Viscosity Parameters in the Large Time Asymptotics of 2D Micropolar Flows

We investigate the role of the four viscosity parameters, in fluids where the particles possess a microstructure (micropolar flows) and are allowed to rotate in a two-dimensional setting. We first establish the existence of global finite energy solutions, satisfying the classical energy equality, for arbitrary initial data in $L^2$, in the case of a spin viscosity $\gamma\ge0$, and we construct the asymptotic profiles of the solution as $t\to+\infty$. We deduce the remarkable fact that the large time behavior only depends on the kinematic viscosity $\mu$, and not on the other parameters $\chi$ (vortex-viscosity), $\gamma$ (spin viscosity) and $\kappa$ (gyroviscosity) of the model. Our primary tool is a new enstrophy-like identity of independent interest, involving the difference between the fluid vorticity and the micro-angular velocity. Another consequence of our analysis is the identification of scenarios where the presence of micro-rotational effects significantly enhances dissipation, thereby slowing down the fluid motion at large times.

math.AP↗

arXiv2026

Asymptotic profiles and large-time behavior for 3D micropolar fluid equations with possibly vanishing spin viscosity

We consider 3D micropolar flows with possible vanishing spin viscosity and investigate the decay of the energy for large times. We compute first the exact $L^2$-asymptotic profile, as $t\to+\infty$, for solutions to the linear 3D micropolar equations, up to the second order. For the nonlinear micropolar system, we first establish the existence of restricted Leray solutions. This new notion of solutions is required because it is not known whether the weak finite energy solutions verify a strong energy inequality. Next, we study the large-time behavior of restricted Leray solutions, and prove that they behave asymptotically in $L^2$ like their linear counterpart, up to the critical algebraic decay rate $O(t^{-5/2})$ for the energy. Applying a remarkable linear enstrophy identity, we show that the microrotation field exhibits faster decay in $L^2$ than the velocity field, allowing us to impose our hypothesis on the velocity field only and not on the angular velocity.

math.AP↗

arXiv2026

The Asymptotic Behaviour of Oldroyd-B Fluids is Almost Newtonian

Consider a viscoelastic fluid of Oldroyd-B type. It is shown that its stress tensor $\tau$ and its Newtonian deformation tensor $D(u)$ decay at the same rate, while the elastic part $\varepsilon=\tau-2\omega D(u)$ decays faster. As a consequence, the stress tensor of a viscoelastic fluid exhibits an almost Newtonian behaviour for large times.

math.AP↗

arXiv2025

Non-Algebraic Decay for Solutions to the Navier-Stokes Equations

Around forty years ago, Michael Wiegner provided, in a seminal paper, sharp algebraic decay rates for solutions of the Navier--Stokes equations, showing that these solutions behave asymptotically like the solutions of the heat equation with the same data as $t\to+\infty$, in the $L^2$-norm, up to some critical decay rate. In the present paper, we close a gap that appears in the conclusion of Wiegner's theorem in the 2D case, for solutions with non-algebraic decay rate.

math.AP↗

arXiv2025

Asymptotic Equivalence and Decay Characterization in Second-Grade Fluid Equations

We establish new asymptotic results for the solutions of the second-grade fluids equations and characterize their decay rate in terms of the behavior of the initial data. Moreover, assuming more regularity for the initial data, we study the large-time behavior of these solutions by comparing them to the solutions of the linearized equations. As a consequence, we obtain lower bounds for the solutions. Other auxiliary results of interest are discussed.

math.AP↗

arXiv2024

Improved decay results for micropolar flows with nonlinear damping

We examine the long-time behavior of solutions (and their derivatives) to the micropolar equations with nonlinear velocity damping. Additionally, we get a speed-up gain of $ t^{1/2} $ for the angular velocity, consistent with established findings for classic micropolar flows lacking nonlinear damping. Consequently, we also obtain a sharper result regarding the asymptotic stability of the micro-rotational velocity $\ww(\cdot,t)$. Related results of independent interest are also included.

math.AP↗

arXiv2022

Upper and lower $\dot{H}^{m}$ estimates for solutions to parabolic equations

In this article we prove results concerning upper and lower decay estimates for homogeneous Sobolev norms of solutions to a rather general family of parabolic equations. Following the ideas of Kreiss, Hagstrom, Lorenz and Zingano, we use eventual regularity of solutions to directly work with smooth solutions in physical space, bootstrapping decay estimates from the $L^2$ norm to higher order derivatives. Besides obtaining upper and lower bounds through this method, we also obtain reverse results: from higher order derivatives decay estimates, we deduce bounds for the $L^2$ norm. We use these general results to prove new decay estimates for some equations and to recover some well known results.

math.AP↗