Details
| Original language | English |
|---|---|
| Article number | 60 |
| Journal | Journal of Mathematical Fluid Mechanics |
| Volume | 26 |
| Issue number | 4 |
| Early online date | 16 Sept 2024 |
| Publication status | Published - Nov 2024 |
Abstract
The chemotaxis-Navier–Stokes system (Formula presented.) modelling the behavior of aerobic bacteria in a fluid drop, is considered in a smoothly bounded domain Ω⊂R2. For all α>0 and all sufficiently regular Φ, we construct global classical solutions and thereby extend recent results for the fluid-free analogue to the system coupled to a Navier–Stokes system. As a crucial new challenge, our analysis requires a priori estimates for u at a point in the proof when knowledge about n is essentially limited to the observation that the mass is conserved. To overcome this problem, we also prove new uniform-in-time Lp estimates for solutions to the inhomogeneous Navier–Stokes equations merely depending on the space-time L2 norm of the force term raised to an arbitrary small power.
Keywords
- 35Q92, 92C17, Chemotaxis, Navier–Stokes, Primary 35K65, Secondary 35Q55, Signal-dependant motility
ASJC Scopus subject areas
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of Mathematical Fluid Mechanics, Vol. 26, No. 4, 60, 11.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Uniform Lp Estimates for Solutions to the Inhomogeneous 2D Navier–Stokes Equations and Application to a Chemotaxis–Fluid System with Local Sensing
AU - Fuest, Mario
AU - Winkler, Michael
N1 - Publisher Copyright: © The Author(s) 2024.
PY - 2024/11
Y1 - 2024/11
N2 - The chemotaxis-Navier–Stokes system (Formula presented.) modelling the behavior of aerobic bacteria in a fluid drop, is considered in a smoothly bounded domain Ω⊂R2. For all α>0 and all sufficiently regular Φ, we construct global classical solutions and thereby extend recent results for the fluid-free analogue to the system coupled to a Navier–Stokes system. As a crucial new challenge, our analysis requires a priori estimates for u at a point in the proof when knowledge about n is essentially limited to the observation that the mass is conserved. To overcome this problem, we also prove new uniform-in-time Lp estimates for solutions to the inhomogeneous Navier–Stokes equations merely depending on the space-time L2 norm of the force term raised to an arbitrary small power.
AB - The chemotaxis-Navier–Stokes system (Formula presented.) modelling the behavior of aerobic bacteria in a fluid drop, is considered in a smoothly bounded domain Ω⊂R2. For all α>0 and all sufficiently regular Φ, we construct global classical solutions and thereby extend recent results for the fluid-free analogue to the system coupled to a Navier–Stokes system. As a crucial new challenge, our analysis requires a priori estimates for u at a point in the proof when knowledge about n is essentially limited to the observation that the mass is conserved. To overcome this problem, we also prove new uniform-in-time Lp estimates for solutions to the inhomogeneous Navier–Stokes equations merely depending on the space-time L2 norm of the force term raised to an arbitrary small power.
KW - 35Q92
KW - 92C17
KW - Chemotaxis
KW - Navier–Stokes
KW - Primary 35K65
KW - Secondary 35Q55
KW - Signal-dependant motility
UR - http://www.scopus.com/inward/record.url?scp=85204289722&partnerID=8YFLogxK
U2 - 10.1007/s00021-024-00899-8
DO - 10.1007/s00021-024-00899-8
M3 - Article
AN - SCOPUS:85204289722
VL - 26
JO - Journal of Mathematical Fluid Mechanics
JF - Journal of Mathematical Fluid Mechanics
SN - 1422-6928
IS - 4
M1 - 60
ER -