Related papers: The 2-D stochastic Keller-Segel particle model : e…
We investigate the one-dimensional Keller-Segel model where the diffusion is replaced by a non-local operator, namely the fractional diffusion with exponent $0<\alpha\leq 2$. We prove some features related to the classical two-dimensional…
We consider the dynamics of finite systems of point masses which move along the real line. We suppose the particles interact pairwise and undergo perfectly inelastic collisions when they collide. In particular, once particles collide, they…
For the parabolic-elliptic Keller-Segel system in R^2 it has been proved that if the initial mass is less than 8\pi/\chi\ global solution exist and in the case that the initial mass is larger than 8\pi/\chi\ blow-up happens. The case of…
We consider a Keller-Segel model coupled to the incompressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of regular solutions and present some blow-up criteria for both cases that…
Strong existence and pathwise uniqueness of solutions with $L^{\infty}$-vorticity of 2D stochastic Euler equations is proved. The noise is multiplicative and involves first derivatives. A Lagrangian approach is implemented, where a…
We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…
This paper is concerned with the uniqueness of solutions to the following nonlocal semi-linear elliptic equation \begin{equation}\label{ellip}\tag{$\ast$} \Delta u-\beta u+\lambda\frac{e^u}{\int_{\Omega}e^u}=0~\mathrm{in}~\Omega,…
In finite-dimensional dynamical systems, stochastic stability provides the selection of physical relevant measures from the myriad invariant measures of conservative systems. That this might also apply to infinite-dimensional systems is the…
We discuss a stochastic interacting particles' system connected to dyadic models of turbulence, defining suitable classes of solutions and proving their existence and uniqueness. We investigate the regularity of a particular family of…
We study finite and countably infinite systems of stochastic differential equations, in which the drift and diffusion coefficients of each component (particle) are determined by its rank in the vector of all components of the solution. We…
In this paper, we propose and study a stochastic aggregation-diffusion equation of the Keller-Segel (KS) type for modeling the chemotaxis in dimensions $d=2,3$. Unlike the classical deterministic KS system, which only allows for…
In this work we obtain rates of convergence for two moderately interacting stochastic particle systems with singular kernels associated to the viscous Burgers and Keller-Segel equations. The main novelty of this work is to consider a…
The parabolic-elliptic Keller-Segel equation with sensitivity saturation, because of its pattern formation ability, is a challenge for numerical simulations. We provide two finite-volume schemes whose goals are to preserve, at the discrete…
The present paper deals with the parabolic-elliptic Keller-Segel equation in the plane in the general framework of weak (or ''free energy") solutions associated to initial datum with finite mass $M$, finite second moment and finite entropy.…
The present paper deals with the parabolic-parabolic Keller-Segel equation in the plane inthe general framework of weak (or "free energy") solutions associated to an initial datum with finite mass $M\textless{} 8\pi$, finite second…
We apply a duality method to prove an optimal stability theorem for the logarithmic Hardy-Littlewood-Sobolev inequality, and we apply it to the estimation of the rate of approach to equilibrium for the critical mass Keller-Segel system.
In this paper, we study the stochastic degenerate Keller-Segel system perturbed by linear multiplicative noise in a bounded domain $\mathcal{O}$. We establish the global existence of martingale solutions for this model with any nonnegative…
We show that the one-dimensional fully parabolic Keller-Segel system with nonlinear diffusion possesses global-in-time solutions, provided the nonlinear diffusion is equal to (1+u)^{-\alpha}, for \alpha < 1, independently on the volume of…
This paper is concerned with a chemotaxis aggregation model for cells, more precisely with a parabolic-elliptic semilinear Patlak-Keller-Segel system in a ball of $\mathbb{R}^N$ for $N\geq 2$. For $N=2$, this system is well known for its…
We show that the Cauchy problem associated with the parabolic-elliptic Keller-Segel model is locally ill-posed in $L^q(\mathbb{R}^n)$ for dimensions $n \in \{3,\dots,9\}$ and throughout the supercritical range $q\in [1,\frac{n}{2})$. The…