Salvatore Rionero

A note on the existence and uniqueness of solutions of the micropolar fluid equations

Abstract We show that existence and uniqueness theorems, known in the theory of the Navier-Stokes equations, are valid for the incompressible micropolar equations too.

Weighted Energy Methods in Fluid Dynamics and Elasticity

Introductory topics on stability of viscous flows.- Energy methods in unbounded domains: The case of a half space.- Energy methods in unbounded domains: The case of an exterior domain.- Some properties of steady solutions in exterior domatins.- Exchange of stabilities, symmetry and the connection between linear and nonlinear stability.- Skew-symmetric operators and nonlinear stabilization: The hydromagnetic benard problem.- Weighted energy methods in elastostatics on unbounded domains.- Weighted energy methods in linear elastodynamics in unbounded domains.

Metodi variazionali per la stabilità asintotica in media in magnetoidrodinamica

SuntoServendosi di una formulazione variazionale si stabiliscono le migliori condizioni sufficienti per la stabilità asintotica in media in magnetoidrodinamica ottenibili con procedimenti di maggiorazione dell’energia della generica perturbazione. Viene considerato in particolare il caso che il campo magnetico imperturbato sia irrotazionale applicando poi i risultati ottenuti in tal caso al moto alla Couette.

THE LAGRANGE IDENTITY METHOD IN LINEAR THERMOELASTICITY

Abstract Coupling the Lagrange identity method with the weight function method, uniqueness and continuous dependence theorems in bounded and exterior domains in linear thermoelasticity are obtained. Recourse to an energy conservative law or to any boundedness or definiteness assumptions on the thermoelastic coefficients is avoided.

On the nonlinear stability of the rotating Bénard problem via the Lyapunov direct method

Abstract In this paper we use the Lyapunov direct method to study the nonlinear conditional stability of the Benard problem with rotation. In particular, for Prandtl numbers greater than or equal to one, and for Taylor numbers less than or equal to 80π4, we prove the coincidence between the linear and nonlinear critical stability parameters. We also give some values of the attracting radius for the conditionally stable disturbances of the basic motion.

Convection in a porous medium with internal heat source and variable gravity effects

Abstract The problem is studied of convection in a fluid saturated porous layer which is heated internally and where the gravitational field varies with distance through the layer. For this problem it is not known whether exchange of stabilities holds. We here find critical Rayleigh numbers for both linear instability and nonlinear energy stability, and numerical findings indicate that for the heat sources and gravity fields chosen, the growth rate of linear theory is real at criticality.

On the Lyapunov stability for SIRS epidemic models with general nonlinear incidence rate

Abstract We study an epidemic model for infections with non permanent acquired immunity (SIRS). The incidence rate is assumed to be a general nonlinear function of the susceptibles and the infectious classes. By using a peculiar Lyapunov function, we obtain necessary and sufficient conditions for the local nonlinear stability of equilibria. Conditions ensuring the global stability are also obtained. Unlike the recent literature on this subject, here no restrictions are required about the monotonicity and concavity of the incidence rate with respect to the infectious class. Among the applications, the noteworthy case of a convex incidence rate is provided.

Global stability in the Bénard problem for a mixture with superimposed plane parallel shear flows

The Lyapunov direct method is used to study the non-linear stability of parallel convective shear flows of a mixture heated and salted from below for any Schmidt and Prandtl numbers. Global non-linear exponential stability for small values of Reynolds number R is found and conditional stability results up to the criticality which are independent of R are given for rigid and stress-free boundaries. Copyright

A uniqueness theorem for hydrodynamic flows in unbounded domains

SummaryWe prove a uniqueness theorem for hydrodynamic motions in unbounded domains, which improves previous theorems.

On the instability of double diffusive convection in porous media under boundary data periodic in space

The linear instability analysis of the motionless state for a binary fluid mixture in a porous layer, under horizontal periodic temperature and concentration gradients, is performed.