Related papers: Suppression of chemotactic singularity by buoyancy
Motivated by the use of Taylor-Couette flow in extracorporeal circulation devices [K$\ddot{\rm o}$rfer et al., 2003, 26(4): 331-338], where it leads to an accumulation of platelets and plasma proteins in the vortex center and therefore to a…
In this paper we consider the parabolic-parabolic Patlak-Keller-Segel models in $\mathbb{T}\times\mathbb{R}$ with advection by a large strictly monotone shear flow. Without the shear flow, the model is $L^1$ critical in two dimensions with…
The hydrodynamic limit for a kinetic model of chemotaxis is investigated. The limit equation is a non local conservation law, for which finite time blow-up occurs, giving rise to measure-valued solutions and discontinuous velocities. An…
In this paper, we study the Cauchy problem of the Poiseuille flow of full Ericksen-Leslie model for nematic liquid crystals. The model is a coupled system of a parabolic equation for the velocity and a quasilinear wave equation for the…
This paper is devoted to the analysis of non-negative solutions for a degenerate parabolic-elliptic Patlak-Keller-Segel system with critical nonlinear diffusion in a bounded domain with homogeneous Neumann boundary conditions. Our aim is to…
In this paper we study the effect of the addition of a convective term, and of the resulting increased dissipation rate, on the growth of solutions to a general class of non-linear parabolic PDEs. In particular, we show that blow-up in…
We revisit the question of global regularity for the Patlak-Keller-Segel (PKS) chemotaxis model. The classical 2D hyperbolic-elliptic model blows up for initial mass M>8\pi. We consider more realistic scenario which takes into account the…
Thermodynamically consistent models for two-phase flow in porous media have attracted significant attention in recent years. In this paper, we prove the existence, uniqueness and regularity of the weak solution to such a recent model…
The Patlak-Keller-Segel equation is a canonical model of chemotaxis to describe self-organized aggregation of organisms interacting with chemical signals. We investigate a variant of this model, assuming that the organisms exert effective…
In this paper, we study the dynamics of a finite number of spherical bubbles in a compressible fluid within a bounded open domain of R 3 . The fluid-bubble interaction is described by a system of nonlinear partial differential equations…
The limiting case of the system of equations of two-dimensional gas dynamics in the presence of the Coriolis force, which can be obtained under the assumption of a small pressure, is considered. With this approach, the equation for the…
In this paper, we consider the Cauchy problem for a generalized parabolic-elliptic Keller-Segel equation with a fractional dissipation and advection by a weakly mixing (see Definition \ref{def:2.4}). Here the attractive kernel has strong…
We consider the interaction of a viscous incompressible fluid with a flexible shell in three space dimensions. The fluid is described by the three-dimensional incompressible Navier--Stokes equations in a domain that is changing in…
We consider the stationary Keller-Segel system from chemotaxis in a ball and we show the existence of a solution concentrating at the boundary of the ball.
We study the regularity and large-time behavior of a crowd of species driven by chemo-tactic interactions. What distinguishes the different species is the way they interact with the rest of the crowd: the collective motion is driven by…
The existence of global weak solutions to the compressible Navier-Stokes equations for the density of endothelial cells and their velocity, coupled to a reaction-diffusion equation for the concentration of the chemoattractant, is…
We prove the uniqueness of H\"older continuous weak solutions via duality argument and vanishing viscosity method for the Keller-Segel system of porous medium type equations coupled to the Stokes system in dimensions three. An important…
We study a system of two coupled nonlinear parabolic equations. It constitutes a variant of the Keller-Segel model for chemotaxis, i.e. it models the behaviour of a population of bacteria that interact by means of a signalling substance. We…
We study a system of interacting diffusions that models chemotaxis of biological cells or microorganisms (referred to as particles) in a chemical field that is dynamically modified through the collective contributions from the particles.…
In this paper we investigate the one-dimensional parabolic-parabolic Patlak-Keller-Segel model of chemotaxis. For the case when the diffusion coefficient of chemical substance is equal to two, in terms of travelling wave variables the…