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Luca Bisconti

Publications and source records attributed to Luca Bisconti.

At least 19 recordsLinked to original sources
arXiv2024

Vanishing viscosity limit for the compressible Navier-Stokes equations with non-linear density dependent viscosities

In a three-dimensional bounded domain $\Omega$ we consider the compressible Navier-Stokes equations for a barotropic fluid with general non-linear density dependent viscosities and no-slip boundary conditions. A nonlinear drag term is added to the momentum equation. We establish two conditional Kato-type criteria for the convergence of the weak solutions to such a system towards the strong solution of the compressible Euler system when the viscosity coefficient and the drag term parameter tend to zero.

math.AP↗
arXiv2023

Global existence for a 3D Tropical Climate Model with damping and small initial data in $\dot H^{1/2}(\mathbb{R}^3)$

We consider a 3D Tropical Climate Model with damping terms in the equation of the barotropic mode $u$ and in the equation of the first baroclinic mode $v$ of the velocity. The equation for the temperature $\theta$ is free from dampings. We prove global existence in time for this system assuming the initial data $(u_0, v_0,\theta_0)$ small, in terms of the homogeneous space $\dot H^{1/2}(\mathbb{R}^3)$.

math.AP↗
arXiv2022

A regularity criterion for a 3D tropical climate model with damping

In this paper we deal with the 3D tropical climate model with damping terms in the equation of the barotropic mode $u$ and in the equation of the first baroclinic mode $v$ of the velocity, and we establish a regularity criterion for this system thanks to which the local smooth solution $(u, v, θ)$ can actually be extended globally in time.

math.AP↗
arXiv2022

Inviscid limit for the compressible Navier-Stokes equations with density dependent viscosity

We consider the compressible Navier-Stokes system describing the motion of a barotropic fluid with density dependent viscosity confined in a three-dimensional bounded domain $Ω$. We show the convergence of the weak solution to the compressible Navier-Stokes system to the strong solution to the compressible Euler system when the viscosity and the damping coefficients tend to zero.

math.AP↗
arXiv2018

On a nonlinear parabolic problem: Stability properties of Ground States

We consider the Cauchy-problem for the following parabolic equation: \begin{equation*} \displaystyle u_t = Δu+ f(u,|x|), \end{equation*} where $x \in \mathbb{R}^n$, $n >2$, and $f=f(u,|x|)$ is either critical or supercritical with respect to the Joseph-Lundgren exponent. Using a new unifying approach we extend to a larger class of nonlinear potentials $f$, some known results concerning stability and weak asymptotic stability of positive Ground States.

math.AP↗
arXiv2015

Existence results in the linear dynamics of quasicrystals with phason diffusion and non-linear gyroscopic effects

Quasicrystals are characterized by quasi-periodic arrangements of atoms. The description of their mechanics involves deformation and a (so called phason) vector field accounting at macroscopic scale of local phase changes, due to atomic flips necessary to match quasi-periodicity under the action of the external environment. Here we discuss the mechanics of quasicrystals, commenting the shift from its initial formulation, as standard elasticity in a space with dimension twice the ambient one, to a more elaborated setting avoiding physical inconveniences of the original proposal. In the new setting we tackle two problems. First we discuss the linear dynamics of quasicrystals including a phason diffusion. We prove existence of weak solutions and their uniqueness under rather general boundary and initial conditions. We then consider phason rotational inertia, non-linearly coupled with the curl of the macroscopic velocity, and prove once again existence of weak solutions to the pertinent balance equations.

math-ph↗
arXiv2015

On a non-homogeneous and non-linear heat equation

We consider the Cauchy-problem for a parabolic equation of the following type: \begin{equation*} \frac{\partial u}{\partial t}= Δu+ f(u,|x|), \end{equation*} where $f=f(u,|x|)$ is supercritical. We supply this equation by the initial condition $u(x,0)=ϕ$, and we allow $ϕ$ to be either bounded or unbounded in the origin but smaller than stationary singular solutions. We discuss local existence and long time behaviour for the solutions $u(t,x;ϕ)$ for a wide class of non-homogeneous non-linearities $f$. We show that in the supercritical case, Ground States with slow decay lie on the threshold between blowing up initial data and the basin of attraction of the null solution. Our results extend previous ones allowing Matukuma-type potential and more generic dependence on $u$. Then, we further explore such a threshold in the subcritical case too. We find two families of initial data $ζ(x)$ and $ψ(x)$ which are respectively above and below the threshold, and have arbitrarily small distance in $L^{\infty}$ norm, whose existence is new even for $f(u,r)=u^{q-1}$. Quite surprisingly both $ζ(x)$ and $ψ(x)$ have fast decay (i.e. $\sim |x|^{2-n}$), while the expected critical asymptotic behavior is slow decay (i.e. $\sim |x|^{2/q-2}$).

math.AP↗
arXiv2014

Periodic perturbations with delay of coupled differential equations on manifolds with application to a sunflower-like equation

We investigate the structure of the set of $T$-periodic solutions to periodically perturbed coupled delay differential equations on differentiable manifolds. By using fixed point index and degree-theoretic methods we prove the existence of branches of $T$-periodic solutions to the considered equations. As main application of our methods, we study a generalized version of the sunflower equation.

math.CA↗
arXiv2014

About the notion of non-$T$-resonance and applications to topological multiplicity results for ODEs on differentiable manifolds

By using topological methods, mainly the degree of a tangent vector field, we establish multiplicity results for $T$-periodic solutions of parametrized $T$-periodic perturbations of autonomous ODEs on a differentiable manifold $M$. In order to provide insights into the key notion of $T$-resonance, we consider the elementary situations $M = \mathbb{R}$ and $M = \mathbb{R}^2$. So doing, we provide more comprehensive analysis of those cases and find improved conditions.

math.CA↗
arXiv2014

Global Attractor for the Navier-Stokes Equations with horizontal filtering

We consider a Large Eddy Simulation model for a homogeneous incompressible Newtonian fluid in a box space domain with periodic boundary conditions on the lateral boundaries and homogeneous Dirichlet conditions on the top and bottom boundaries, thus simulating a horizontal channel. The model is obtained through the application of an anisotropic horizontal filter, which is known to be less memory consuming from a numerical point of view, but provides less regularity with respect to the standard isotropic one defined as the inverse of the Helmholtz operator. It is known that there exists a unique regular weak solution to this model that depends weakly continuously on the initial datum. We show the existence of the global attractor for the semiflow given by the time-shift in the space of paths. We prove the continuity of the horizontal components of the flow under periodicity in all directions and discuss the possibility to introduce a solution semiflow.

math.AP↗
arXiv2013

Periodic solutions of semi-explicit differential-algebraic equations with time-dependent constraints

In this paper we investigate the properties of the set of T-periodic solutions of semi-explicit parametrized Differential-Algebraic Equations with non-autonomous constraints of a particular type. We provide simple, degree theoretic conditions for the existence of branches of T-periodic solutions of the considered equations. Our approach is based on topological arguments about differential equations on implicitly defined manifolds, combined with elementary facts of matrix analysis.

math.CA↗
arXiv2013

On the convergence of an approximate deconvolution model to the 3D mean Boussinesq equations

In this paper we study a Large Eddy Simulation (LES) model for the approximation of large scales of the 3D Boussinesq equations. This model is obtained using the approach first described by Stolz and Adams, based on the Van Cittern approximate deconvolution operators, and applied to the filtered Boussinesq equations. Existence and uniqueness of a regular weak solution are provided. Our main objective is to prove that this solution converges towards a solution of the filtered Boussinesq equations, as the deconvolution parameter goes to zero.

math.AP↗
arXiv2012

On a class of differential-algebraic equations with infinite delay

We study the set of $T$-periodic solutions of a class of $T$-periodically perturbed Differential-Algebraic Equations, allowing the perturbation to contain a distributed and possibly infinite delay. Under suitable assumptions, the perturbed equations are equivalent to Retarded Functional (Ordinary) Differential Equations on a manifold. Our study is based on known results about the latter class of equations.

math.CA↗