Related papers: A global existence result for a Keller-Segel type …
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…
We study the global existence of solutions to the Cauchy problem for the two-dimensional fully parabolic Keller--Segel system at the critical mass. It is known that global-in-time existence holds for initial data with critical mass under…
As it is well known, the parabolic-elliptic Keller-Segel system of chemotaxis on the plane has global-in-time regular nonnegative solutions with total mass below the critical value $8\pi$. Solutions with mass above $8\pi$ blow up in a…
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…
In the present article we consider several issues concerning the doubly parabolic Keller-Segel system in the plane, when the initial data belong to critical scaling-invariant Lebesgue spaces. More specifically, we analyze the global…
The paper should be viewed as complement of an earlier result in [8]. In the paper just mentioned it is shown that 1d case of a quasilinear parabolic-elliptic Keller-Segel system is very special. Namely, unlike in higher dimensions, there…
In this paper, we investigate global existence of large solutions for the parabolic-elliptic Keller-Segel system in the homogeneous Besov type spaces. A class of initial data was presented, generating a global smooth solution although the…
We consider a two dimensional parabolic-elliptic Keller-Segel equation with a logistic forcing and a fractional diffusion of order $\alpha$. We obtain existence of global in time regular solution for arbitrary initial data with no size…
We study the global existence of the parabolic-parabolic Keller-Segel system in $\R^d , d \ge 2$. We prove that initial data of arbitrary size give rise to global solutions provided the diffusion parameter $\tau$ is large enough in the…
This paper deals with the fully parabolic chemotaxis system of local sensing in higher dimensions. Despite the striking similarity between this system and the Keller--Segel system, we prove the absence of finite-time blow-up phenomenon in…
We study the global in time existence and long time asymptotics of solutions to the parabolic-elliptic Patlak-Keller-Segel system for the multi-species populations in the whole Euclidean space $\mathbb{R}^2.$ We prove that at the borderline…
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…
It is known that solutions of the parabolic elliptic Keller-Segel equations in the two dimensional plane decay, as time goes to infinity, provided the initial data admits sub-critical mass and finite second moments, while such solution…
In this paper we consider quasilinear Keller-Segel type systems of two kinds in higher dimensions. In the case of a nonlinear diffusion system we prove an optimal (with respect to possible nonlinear diffusions generating explosion in finite…
The existence of generalised global supersolutions with a control upon the total muss is established for the parabolic-parabolic Keller-Segel system with logarithmic sensitivity for any space dimension. It is verified that smooth…
The L^1-critical parabolic-elliptic Patlak-Keller-Segel system is a classical model of chemotactic aggregation in micro-organisms well-known to have critical mass phenomena. In this paper we study this critical mass phenomenon in the…
This paper is devoted mainly to the global existence problem for the two-dimensional parabolic-parabolic Keller-Segel in the full space. We derive a critical mass threshold below which global existence is ensured. Using carefully energy…
In this paper we consider a stochastic Keller-Segel type equation, perturbed with random noise. We establish that for special types of random pertubations (i.e. in a divergence form), the equation has a global weak solution for small…
In two space dimensions, the parabolic-parabolic Keller--Segel system shares many properties with the parabolic-elliptic Keller--Segel system. In particular, solutions globally exist in both cases as long as their mass is less than 8?.…
A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than $8\pi$ as the initial data is given. This result has been obtained by Senba--Suzuki and Bedrossian--Masmoudi…