391 citations · 668 across the 36 of their papers we have counts for
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Does fluid interaction affect regularity in the three-dimensional Keller-Segel system with saturated sensitivity?
Michael Winkler
A class of Keller-Segel-Stokes systems generalizing the prototype \[ \left\{ \begin{array}{rcl} n_t + u\cdot\nabla n &=& Δn - \nabla \cdot \Big(n(n+1)^{-α}\nabla c\Big), c_t + u\cd…
Migration-driven benefit in a two-species nutrient taxis system
Piotr Krzyzanowski, Michael Winkler, Dariusz Wrzosek
A model describing the competition of two species for a common nutrient is studied. It is assumed that one of the competitors is motionless while the other has the ability to move…
Counterintuitive dependence of temporal asymptotics on initial decay in a nonlocal degenerate parabolic equation arising in game theory
Johannes Lankeit, Michael Winkler
We consider the degenerate parabolic equation with nonlocal source given by \[ u_t=uΔu + u \int_{\mathbb{R}^n} |\nabla u|^2, \] which has been proposed as model for the evolution o…
The fast signal diffusion limit in Keller-Segel(-fluid) systems
Yulan Wang, Michael Winkler, Zhaoyin Xiang
This paper deals with convergence of solutions to a class of parabolic Keller-Segel systems, possibly coupled to the (Navier-)Stokes equations in the framework of the full model \b…
Blow-up profiles for the parabolic-elliptic Keller-Segel system in dimensions
Philippe Souplet, Michael Winkler
We study the blow-up asymptotics of radially decreasing solutions of the parabolic-elliptic Keller-Segel-Patlak system in space dimensions . In view of the biological backg…