Analysis of a stochastic SIR model with fractional Brownian motion

In this article, a stochastic version of a SIR nonautonomous model previously introduced in Kloeden and Kozyakin (2011) is considered. The noise considered is a fractional Brownian motion which satisfies the property of long range memory, which roughly implies that the decay of stochastic dependence with respect to the past is only subexponentially slow, what makes this kind of noise a realistic choice for problems with long memory in the applied sciences. The stochastic model containing a standard Brownian motion has been studied in Caraballo and Colucci (2016). In this paper, we analyze the existence and uniqueness of solutions to our stochastic model as well as their positiveness.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalJunta de Andalucí

Semi classical limit for a NLS with potential

This paper is dedicated to the semiclassical limit of t the nonlinear focusing Schrödinger equation (NLS) with a potential , i\e\partial_t u^{\e}+\frac{\e^2}{2}\lap u^{\e}-V(x)u^{\e}+|u^{\e}|^{2\sigma}u^{\e}=0 with initial data in the form Q\left(\frac{x-x_0}{\e}\right)e^{i\frac{x.v_0}{\e}}, where $Q$ is the ground state of the associated unscaled elliptic problem. Using a refined version of the method introduced in \cite{BJ} by J. C. Bronski, R.L. Jerrard, we prove that, up to a time-dependent phase shift, the initial shape is conserved with parameters that are transported by the classical flow of the classical Hamiltonian $H(t,x)=\frac{|\xi|^2}{2}+V( x)$. This gives, in particular, a complete description of the dynamics of the time-dependent Wigner measure associated to the family of solutions

On the global existence for the axisymmetric Euler equations

This paper deals with the global well-posedness of the 3D axisymmetric Euler equations for initial data lying in some critical Besov spacesComment: 14 page

Limite non visqueuse pour le système de Navier-Stokes dans un espace critique

International audienceDans un article récent [11], Vishik montre que le système d'Euler bidimensionnel est globalement bien posé dans l'espace de Besov critique $B^2_{2,1}$. Nous montrons ici que le système de Navier-Stokes est globalement bien posé dans $B^2_{2,1}$, avec des estimations uniformes par rapport à la viscosité. Nous prouvons également un résultat global de limite non visqueuse. Le taux de convergence dans $L^2$ est de l'ordre $\nu$