Analysis of chemotactic migration in liquid environments / Tobias Black. Paderborn, 2019
Content
- Introduction
- Sublinear signal production in a two-dimensional Keller–Segel–Stokes system
- Introduction
- Local existence of classical solutions
- Regularity of u implied by regularity of n
- Global existence and boundedness in two-dimensional domains
- Global solvability of chemotaxis fluid systems with nonlinear diffusion and matrix-valued sensitivities in three dimensions
- Introduction
- The notions of weak and very weak solutions
- A family of regularized problems
- A priori estimates
- Estimates capturing optimal conditions on m and alpha
- Estimates involving the fluid component
- Time regularity
- Limit functions and their regularity properties
- Solution properties of the limit functions
- Eventual smoothness of generalized solutions to a singular chemotaxis-Stokes system in 2D
- Introduction
- Basic properties of a family of generalized problems
- Generalized solution concept and approximate solutions
- Eventual smoothness of small-data generalized solutions
- The Stokes limit in a three-dimensional chemotaxis-Navier–Stokes system
- Introduction
- Preliminaries. Weak solutions and a priori information for a family of approximating systems
- Existence of a limit solution family when epsilon to zero
- Eventual smallness of oxygen concentration with waiting times independent of eps and kappa
- Eventual Lp regularity estimates independent of eps and kappa as consequence of small oxygen concentration
- Uniform eventual stabilization of nepkap and uepkap in some Lp spaces
- Uniform eventual smoothness estimates
- Uniform exponential decay after the smoothing time
- The second limit. Taking kappa to zero
- Bibliography