Related papers: Homogenization of weakly coercive integral functio…

One of the principal difficulties in stochastic homogenization is transferring quantitative ergodic information from the coefficients to the solutions, since the latter are nonlocal functions of the former. In this paper, we address this…

We derive, via simultaneous homogenization and dimension reduction, the Gamma-limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much smaller than, the film thickness. We consider the…

In this paper, we introduce a model describing the dynamic of vesicle membranes within an incompressible viscous fluid in $3D$ domains. The system consists of the Navier-Stokes equations, with an extra stress tensor depending on the…

In the local density approximation (LDA) for electronic time-dependent current-density functional theory (TDCDFT) many-body effects are described in terms of the visco-elastic constants of the homogeneous three-dimensional electron gas. In…

We study the $\Gamma$-convergence of sequences of free-discontinuity functionals depending on vector-valued functions $u$ which can be discontinuous across hypersurfaces whose shape and location are not known a priori. The main novelty of…

Partial localization is the phenomenon of self-aggregation of mass into high-density structures that are thin in one direction and extended in the others. We give a detailed study of an energy functional that arises in a simplified model…

We show that relativistic quantum electrodynamics in the Coulomb gauge satisfies the following bound, which establishes stability: let $H(\Lambda,V)$ denote the Hamiltonian of $QED_{1+3}$ on the three-dimensional torus of volume $V$ and…

In this study, we consider three dark energy models in which $\Lambda$ is not constant, but has a dynamic nature that depends on the Hubble parameter $H$ and/or its time derivative $\dot{H}$. We analyze the generalized running vacuum model,…

We study the energy balance for weak solutions of the three-dimensional compressible Navier--Stokes equations in a bounded domain. We establish an $L^p$-$L^q$ regularity conditions on the velocity field for the energy equality to hold,…

The fundamental constants of electromagnetism, gravity and quantum mechanics can be related empirically by the numerical approximation $\ln(V_e/V_P)\approx \alpha^{-1}$, where $\alpha$ is the low energy value of the electromagnetic fine…

In this paper we derive, by means of $\Gamma$-convergence, the shallow shell models starting from non linear three dimensional elasticity. We use the approach analogous to the one for shells and plates. We start from the minimization…

The paper considers the general case of incompressible non-classical elasticity with small deformations and rotations. The thermodynamic stability is analysed for free energy density with three rotational degrees of freedom. Although the…

We consider a finite region of a $d$-dimensional lattice, $d\in\mathbb{N}$, of weakly coupled harmonic oscillators. The coupling is provided by a nearest-neighbour potential (harmonic or not) of size $\varepsilon$. Each oscillator weakly…

Regularity and uniqueness of weak solutions of the compressible barotropic Navier-Stokes equations with constant viscosity coefficients is proven for small time in dimension $N=2,3$ under periodic boundary conditions. In this paper, the…

We validate the Timoshenko beam model as an approximation of the linear-elasticity model of a three-dimensional beam-like body. Our validation is achieved within the framework of $\Gamma$-convergence theory, in two steps: firstly, we…

We address the global-in-time existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. We show the details of the $\alpha$-dependence of different…

We show that, in the periodic homogenization of uniformly elliptic Hamilton-Jacobi equations in any dimension, the effective Hamiltonian does not necessarily inherit the quasiconvexity property (in the momentum variables) of the original…

We prove the existence of weak solutions to the 3D ideal MHD equations, of class $C^\alpha$ with $\alpha=1/200$, for which the total energy and the cross helicity (i.e., the so-called Els\"asser energies) are not conserved. The solutions do…

In heterotic flux compactification with supersymmetry, three different connections with torsion appear naturally, all in the form $\omega+a H$. Supersymmetry condition carries $a=-1$, the Dirac operator has $a=-1/3$, and higher order term…

We consider an abstract second order linear equation with a strong dissipation, namely a friction term which depends on a power of the "elastic" operator. In the homogeneous case, we investigate the phase spaces in which the initial value…