Michael Winkler

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math.AP2024

A switch in dimension dependence of critical blow-up exponents in a Keller-Segel system involving indirect signal production

Youshan Tao, Michael Winkler

In bounded $n$ -dimensional domains with $n \geq 3$ , this manuscript considers an initial-boundary problem for a quasilinear chemotaxis system with indirect attractant production, as…

math.AP2024

Uniform $L^{p}$ estimates for solutions to the inhomogeneous 2D Navier-Stokes equations and application to a chemotaxis-fluid system with local sensing

Mario Fuest, Michael Winkler

The chemotaxis-Navier-Stokes system \begin{equation*}\label{1} \left\{ \begin{array}{rcl} n_t+u\cdot\nabla n &=& Δ\big(n c^{-α} \big), \\[1mm] c_t+ u\cdot\nabla c &=& Δc -nc,\\[1mm…

math.AP2023

Stability vs. instability of singular steady states in the parabolic-elliptic Keller-Segel system on $R^{n}$

Francesca Colasuonno, Michael Winkler

The Cauchy problem in $R^{n}$ is considered for \begin{eqnarray*} \left\{ \begin{array}{l} u_t = Δu - \nabla \cdot (u\nabla v),\\ 0 = Δv + u. \end{array} \right. \end{eqnarra…

A switch in dimension dependence of critical blow-up exponents in a Keller-Segel system involving indirect signal production

Uniform Lp estimates for solutions to the inhomogeneous 2D Navier-Stokes equations and application to a chemotaxis-fluid system with local sensing

Stability vs. instability of singular steady states in the parabolic-elliptic Keller-Segel system on Rn

Uniform $L^{p}$ estimates for solutions to the inhomogeneous 2D Navier-Stokes equations and application to a chemotaxis-fluid system with local sensing

Stability vs. instability of singular steady states in the parabolic-elliptic Keller-Segel system on $R^{n}$