Analytic solutions of the Navier-Stokes equations

We consider the time dependent incompressible Navier-Stokes equations on an half plane. For analytic initial data, existence and uniqueness of the solution are proved using the Abstract Cauchy-Kovalevskaya Theorem in Banach spaces. The time interval of existence is proved to be independent of the viscosit

Cross-diffusion driven instability in a predator-prey system with cross-diffusion

In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. Finally when the pattern invades the domain as a travelling wavefront, we derive the Ginzburg-Landau amplitude equation which is able to describe the shape and the speed of the wave.Comment: 15 pages, 5 figure

Zero viscosity limit of the Oseen equations in a channel

Oseen equations in the channel are considered. We give an explicit solution formula in terms of the inverse heat operators and of projection operators. This solution formula is used for the analysis of the behavior of the Oseen equations in the zero viscosity limit. We prove that the solution of Oseen equations converges in W1,2 to the solution of the linearized Euler equations outside the boundary layer and to the solution of the linearized Prandtl equations inside the boundary layer. © 2001 Society for Industrial and Applied Mathematics

Well-posedness of the boundary layer equations

We consider the mild solutions of the Prandtl equations on the half space. Requiring analyticity only with respect to the tangential variable, we prove the short time existence and the uniqueness of the solution in the proper function space. The proof is achieved applying the abstract Cauchy-Kowalewski theorem to the boundary layer equations once the convection-diffusion operator is explicitly inverted. This improves the result of [M. Sammartino and R. E. Caflisch, Comm. Math. Phys., 192 (1998), pp. 433-461], as we do not require analyticity of the data with respect to the normal variable

Asymptotic analysis of the linearized Navier-Stokes equation on an exterior circular domain: Explicit solution and the zero viscosity limit

In this paper we study and derive explicit formulas for the linearized Navier-Stokes equations on an exterior circular domain in space dimension two. Through an explicit construction, the solution is decomposed into an inviscid solution, a boundary layer solution and a corrector. Bounds on these solutions are given, in the appropriate Sobolev spaces, in terms of the norms of the initial and boundary data. The correction term is shown to be of the same order of magnitude as the square root of the viscosity. Copyright © 2001 by Marcel Dekker, Inc

CROSS-DIFFUSION EFFECTS ON STATIONARY PATTERN FORMATION IN THE FITZHUGH-NAGUMO MODEL

We investigate the formation of stationary patterns in the FitzHugh-Nagumo reaction-diffusion system with linear cross-diffusion terms. We focus our analysis on the effects of cross-diffusion on the Turing mechanism. Linear stability analysis indicates that positive values of the inhibitor cross-diffusion enlarge the region in the parameter space where a Turing instability is excited. A sufficiently large cross-diffusion coefficient of the inhibitor removes the requirement imposed by the classical Turing mechanism that the inhibitor must diffuse faster than the activator. In an extended region of the parameter space a new phenomenon occurs, namely the existence of a double bifurcation threshold of the inhibitor/activator diffusivity ratio for the onset of patterning instabilities: for large values of inhibitor/activator diffusivity ratio, classical Turing patterns emerge where the two species are in-phase, while, for small values of the diffusion ratio, the analysis predicts the formation of out-of-phase spatial structures (named cross-Turing patterns). In addition, for increasingly large values of the inhibitor cross-diffusion, the upper and lower bifurcation thresholds merge, so that the instability develops independently on the value of the diffusion ratio, whose magnitude selects Turing or cross-Turing patterns. Finally, the pattern selection problem is addressed through a weakly nonlinear analysis

Wavefront invasion for a chemotaxis model of Multiple Sclerosis

In this work we study wavefront propagation for a chemotaxis reaction-diffusion system describing the demyelination in Multiple Sclerosis. Through a weakly non linear analysis, we obtain the Ginzburg–Landau equation governing the evolution of the amplitude of the pattern. We validate the analytical findings through numerical simulations. We show the existence of traveling wavefronts connecting two different steady solutions of the equations. The proposed model reproduces the progression of the disease as a wave: for values of the chemotactic parameter below threshold, the wave leaves behind a homogeneous plaque of apoptotic oligodendrocytes. For values of the chemotactic coefficient above threshold, the model reproduces the formation of propagating concentric rings of demyelinated zones, typical of Baló’s sclerosis

Psychological violence and manipulative behavior in couple: A focus on personality traits

Psychological violence is characterized by systematic denigration and humiliation of the partner (victim). It is an insidious and manipulative behavior put in place to ensure that the victim begins to doubt themselves, and their own judgments, to the point of feeling confused and wrong. This behavior pattern is called Gaslighting and the personality traits are characterized by lack of empathy, psychopathy, narcissism and Machiavellianism. These three conditions are part of the so-called dark triad and distinguished by the lack of empathy. The aim of this study is to explore psychological aspects and consequences of Gaslighting phenomena. This systematic review was conducted according to Systematic Reviews guidelines (PubMed and Google Scholar databases), using 2 key terms related to this topic “Psychological Violence” AND “Gaslighting”. Data for this systematic review were collected in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA). The reviewed studies focused on violence on affective manipulation, abuse trauma that compromises a subject\u27s identity, psyche, self-esteem and sense of self, in women\u27s mental health conditions. Most of the research analyzed is focused on the gender violence and manipulative behavior in couples