# Well-posedness for chemotaxis-fluid models in arbitrary dimensions

@inproceedings{Diebou2021WellposednessFC, title={Well-posedness for chemotaxis-fluid models in arbitrary dimensions}, author={Gael Yomgne Diebou}, year={2021} }

. We study the Cauchy problem for the chemotaxis Navier-Stokes equations and the Keller-Segel-Navier-Stokes system. Local-in-time and global-in-time solutions satisfying fundamental properties such as mass conservation and nonnegativity preservation are constructed for low regularity data in 2 and higher dimensions under suitable conditions. Our initial data classes involve a new scale of function space, that is L − 1 2 ,N − 2 ( R N ) which collects divergence of vector-ﬁelds with components in…

## References

SHOWING 1-10 OF 47 REFERENCES

### Existence and large time behavior to coupled chemotaxis-fluid equations in Besov–Morrey spaces

- MathematicsJournal of Differential Equations
- 2019

### Global well-posedness and asymptotic behavior in Besov-Morrey spaces for chemotaxis-Navier-Stokes fluids

- MathematicsJournal of Mathematical Physics
- 2019

In this work we consider the Keller-Segel system coupled with Navier-Stokes equations in $\mathbb{R}^{N}$ for $N\geq2$. We prove the global well-posedness with small initial data in Besov-Morrey…

### Global Large-Data Solutions in a Chemotaxis-(Navier–)Stokes System Modeling Cellular Swimming in Fluid Drops

- Mathematics
- 2012

In the modeling of collective effects arising in bacterial suspensions in fluid drops, coupled chemotaxis-(Navier–)Stokes systems generalizing the prototype have been proposed to describe the…

### A blow-up mechanism for a chemotaxis model

- Mathematics
- 1997

We consider the following nonlinear system of parabolic equations: (1) ut =Δu−χ∇(u∇v), Γvt =Δv+u−av for x∈B R, t>0. Here Γ,χ and a are positive constants and BR is a ball of radius R>0 in R2. At the…

### Existence of Smooth Solutions to Coupled Chemotaxis-Fluid Equations

- Mathematics
- 2011

We consider a system coupling the parabolic-parabolic Keller-Segel equations to the in- compressible Navier-Stokes equations in spatial dimensions two and three. We establish the local existence of…

### How far do chemotaxis-driven forces influence regularity in the Navier-Stokes system?

- Mathematics
- 2015

The chemotaxis-Navier-Stokes system nt + u · ∇n = ∆n−∇ · (nχ(c)∇c), ct + u · ∇c = ∆c− nf(c), ut + (u · ∇)u = ∆u+∇P + n∇Φ, ∇ · u = 0, (⋆) (0.1) is considered under boundary conditions of…

### Semilinear heat equations and the navier-stokes equation with distributions in new function spaces as initial data

- Mathematics
- 1994

In this paper the authors consider a specified Cauchy problem for semilinear hear equations on [Re][sup n] and also the Cauchy problem for the Navier-Stokes equation on [Re][sup n] for n[ge]2 of a…

### Global Solutions to the Coupled Chemotaxis-Fluid Equations

- Mathematics
- 2010

In this paper, we are concerned with a model arising from biology, which is a coupled system of the chemotaxis equations and the viscous incompressible fluid equations through transport and external…