# On the Navier–Stokes equations on surfaces

@article{Pruess2020OnTN, title={On the Navier–Stokes equations on surfaces}, author={Jan Pruess and Gieri Simonett and Mathias Wilke}, journal={arXiv: Analysis of PDEs}, year={2020} }

We consider the motion of an incompressible viscous fluid that completely covers a smooth, compact and embedded hypersurface $\Sigma$ without boundary and flows along $\Sigma$. Local-in-time well-posedness is established in the framework of $L_p$-$L_q$-maximal regularity. We characterize the set of equilibria as the set of all Killing vector fields on $\Sigma$ and we show that each equilibrium on $\Sigma$ is stable. Moreover, it is shown that any solution starting close to an equilibrium exists…

## 7 Citations

### Nonlinear stability of the two-jet Kolmogorov type flow on the unit sphere under a perturbation with nondissipative part

- Mathematics
- 2022

. We consider the vorticity form of the Navier–Stokes equations on the two-dimensional unit sphere and study the nonlinear stability of the two-jet Kolmogorov type ﬂow which is a stationary solution…

### Tangential Navier-Stokes equations on evolving surfaces: Analysis and simulations

- MathematicsArXiv
- 2022

The paper considers a system of equations that models a lateral flow of a Boussinesq–Scriven fluid on a passively evolving surface embedded in R3. For the resulting Navier-Stokes type system, posed…

### Rate of the Enhanced Dissipation for the Two-jet Kolmogorov Type Flow on the Unit Sphere

- MathematicsJournal of Mathematical Fluid Mechanics
- 2022

We study the enhanced dissipation for the two-jet Kolmogorov type flow which is a stationary solution to the Navier–Stokes equations on the two-dimensional unit sphere given by the zonal spherical…

### Linear stability and enhanced dissipation for the two-jet Kolmogorov type flow on the unit sphere

- MathematicsJournal of Functional Analysis
- 2022

### $H^\infty$-calculus for the surface Stokes operator and applications

- Mathematics
- 2021

We consider a smooth, compact and embedded hypersurface Σ without boundary and show that the corresponding (shifted) surface Stokes operator ω + AS,Σ admits a bounded H ∞-calculus with angle smaller…

### On derivations of evolving surface Navier-Stokes equations

- MathematicsArXiv
- 2021

Five different derivations of surface Navier-Stokes equations are put into one framework and it is shown that some, but not all, of the resulting models are the same.

### A geometric trapping approach to global regularity for 2D Navier-Stokes on manifolds

- Mathematics
- 2020

In this paper, we use frequency decomposition techniques to give a direct proof of global existence and regularity for the Navier-Stokes equations on two-dimensional Riemannian manifolds without…

## References

SHOWING 1-10 OF 33 REFERENCES

### Bacterial aminopeptidases: properties and functions.

- Biology, ChemistryFEMS microbiology reviews
- 1996

The quoted studies demonstrate that bacterial aminopeptidases generally show Michaelis-Menten kinetics and can be placed into either of two categories based on their substrate specificity: broad or narrow.

### Learned control of slow potential interhemispheric asymmetry in schizophrenia.

- Psychology, MedicineInternational journal of psychophysiology : official journal of the International Organization of Psychophysiology
- 1999

### Dynamics of a fluid interface

- Chem. Eng. Sci. 12
- 1960

### Analysis on Morrey Spaces and Applications to Navier-Stokes and Other Evolution Equations

- Mathematics
- 1992

### The stokes equation in the Lp-setting: Well-posedness and regularity properties

- Mathematics
- 2018

This article discusses the Stokes equation in various classes of domains R within the L-setting for 1 p 1 from the point of view of evolution equations. Classical as well as modern approaches to…

### Energetic variational approaches for incompressible fluid systems on an evolving surface

- Mathematics
- 2016

### Optimizing Semantic Coherence in Topic Models

- Computer ScienceEMNLP
- 2011

A novel statistical topic model based on an automated evaluation metric based on this metric that significantly improves topic quality in a large-scale document collection from the National Institutes of Health (NIH).

### The dramatic reality of biliary tract injury during laparoscopic cholecystectomy

- MedicineSurgical Endoscopy
- 1997

Biliary tract injury is associated with significant mortality and complications in the practice of Belgian community surgeons, and the impact of the primary biliary repair on long-term outcome is an argument to refer these patients to specialized multidisciplinary experts.