arXiv subjects

Adriana Valentina Busuioc

Publications and source records attributed to Adriana Valentina Busuioc.

6 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 $γ\ge0$, 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 $μ$, and not on the other parameters $χ$ (vortex-viscosity), $γ$ (spin viscosity) and $κ$ (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↗

arXiv2022

The incompressible $α$--Euler equations in the exterior of a vanishing disk

In this article we consider the $α$--Euler equations in the exterior of a small fixed disk of radius $ε$. We assume that the initial potential vorticity is compactly supported and independent of $ε$, and that the circulation of the unfiltered velocity on the boundary of the disk does not depend on $ε$. We prove that the solution of this problem converges, as $ε\to 0$, to the solution of a modified $α$--Euler equation in the full plane where an additional Dirac located at the center of the disk is imposed in the potential vorticity.

math.AP↗

arXiv2016

Weak solutions for the $α$-Euler equations and convergence to Euler

We consider the limit $α\to0$ for the $α$-Euler equations in a two-dimensional bounded domain with Dirichlet boundary conditions. Assuming that the vorticity is bounded in $L^p$, we prove the existence of a global solution and we show the convergence towards a solution of the incompressible Euler equation with $L^p$ vorticity. The domain can be multiply-connected. We also discuss the case of the second grade fluid when both $α$ and $ν$ go to 0.

math.AP↗

arXiv2016

From second grade fluids to the Navier-Stokes equations

We consider the limit $α\to0$ for a second grade fluid on a bounded domain with Dirichlet boundary conditions. We show convergence towards a solution of the Navier-Stokes equations under two different types of hypothesis on the initial velocity $u_0$. If the product $\|u_0\|_{L^2}\|u_0\|_{H^1}$ is sufficiently small we prove global-in-time convergence. If there is no smallness assumption we obtain local-in-time convergence up to the time $C/\|u_0\|_{H^1}^4$.

math.AP↗

arXiv2011

The FENE dumbbell polymer model: existence and uniqueness of solutions for the momentum balance equation

We consider the FENE dumbbell polymer model which is the coupling of the incompressible Navier-Stokes equations with the corresponding Fokker-Planck-Smoluchowski di ffusion equation. We show global well-posedness in the case of a 2D bounded domain. We assume in the general case that the initial velocity is sufficiently small and the initial probability density is sufficiently close to the equilibrium solution; moreover an additional condition on the coeffcients is imposed. In the corotational case, we only assume that the initial probability density is sufficiently close to the equilibrium solution.

math.AP↗