8 papers
Prescribed signal concentration on the boundary: Weak solvability in a chemotaxis-Stokes system with proliferation
Tobias Black, Chunyan Wu
We study a chemotaxis-Stokes system with signal consumption and logistic source terms of the form \noindent \begin{align*} \left\{ \begin{array}{r@{\ }l@{\quad}l@{\quad}l@{\,}c} n_…
Global generalized solutions to a forager-exploiter model with superlinear degradation and their eventual regularity properties
Tobias Black
In this article we consider a cascaded taxis model for two proliferating and degrading species which thrive on the same nutrient but orient their movement according to different sc…
The Stokes limit in a three-dimensional chemotaxis-Navier-Stokes system
Tobias Black
We consider initial-boundary value problems for the -dependent family of chemotaxis-(Navier--)Stokes systems \begin{align*} \left\{ \begin{array}{r@{\,}c@{\,}c@{\ }l@{\quad}l@{\…
Stabilization in the Keller--Segel system with signal-dependent sensitivity
Tobias Black, Johannes Lankeit, Masaaki Mizukami
This paper deals with the Keller--Segel system with signal-dependent sensitivity \begin{align*} &u_t = Δu - χ\nabla \cdot (uS(v)\nabla v), &v_t = Δv - v + u, \end{align*} where $χ>…
Global solvability of chemotaxis-fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions
Tobias Black
In this work we extend a recent result to chemotaxis fluid systems which include matrix-valued sensitivity functions in addit…
A Keller-Segel-fluid system with singular sensitivity: Generalized solutions
Tobias Black, Johannes Lankeit, Masaaki Mizukami
In bounded smooth domains , , we consider the Keller-Segel-Stokes system \begin{align*} n_t + u\cdot \nabla n &= Δn - χ\nabla \cdot(\frac{n}{c}\n…