# Incompressible Limits of Fluids Excited by Moving Boundaries

@article{Feireisl2014IncompressibleLO, title={Incompressible Limits of Fluids Excited by Moving Boundaries}, author={Eduard Feireisl and Ondřej Kreml and {\vS}{\'a}rka Ne{\vc}asov{\'a} and Jiř{\'i} Neustupa and Jan Stebel}, journal={SIAM J. Math. Anal.}, year={2014}, volume={46}, pages={1456-1471} }

We consider the motion of a viscous compressible fluid confined to a physical space with a time dependent kinematic boundary. We suppose that the characteristic speed of the fluid is dominated by the speed of sound and perform the low Mach number limit in the framework of weak solutions. The standard incompressible Navier--Stokes system is identified as the target problem.

## 7 Citations

On the low Mach number limit of compressible flows in exterior moving domains

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We study the incompressible limit of solutions to the compressible barotropic Navier–Stokes system in the exterior of a bounded domain undergoing a simple translation. The problem is reformulated…

The motion of a compressible viscous fluid around rotating body

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We consider the motion of compressible viscous fluids around a rotating rigid obstacle when the velocity at infinity is non zero and parallel to the axis of rotation. We prove the existence of weak…

Flow of heat conducting fluid in a time-dependent domain

- PhysicsZeitschrift für angewandte Mathematik und Physik
- 2018

We consider a flow of heat conducting fluid inside a moving domain whose shape in time is prescribed. The flow in this case is governed by the Navier–Stokes–Fourier system consisting of equation of…

Low stratification of a heat-conducting fluid in a time-dependent domain

- Mathematics
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We study the low Mach number limit of the full Navier–Stokes–Fourier system in the case of low stratification with ill-prepared initial data for the problem stated on a moving domain with a…

Low mach number limits and acoustic waves

- Physics, Mathematics
- 2018

This review is devoted to the low Mach number limits of the Navier-Stokes equations for the compressible fluids in the context of weak solutions. Acoustic waves play a crucial role in these limits.…

Relative entropy and a weak-strong uniqueness principle for the compressible Navier-Stokes equations on moving domains

- MathematicsAppl. Math. Lett.
- 2016

Low Mach and low Froude number limit for vacuum free boundary problem of all-time classical solutions of 1-D compressible Navier-Stokes equations

- Mathematics
- 2020

In this paper, we study the low Mach and Froude number limit for the all-time classical solution of a fluid-vacuum free boundary problem of one-dimensional compressible Navier-Stokes equations. No…

## References

SHOWING 1-10 OF 20 REFERENCES

On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions

- Mathematics
- 2010

We study the low Mach number limit for the compressible
Navier-Stokes system supplemented with Navier's boundary condition
on an unbounded domain with compact boundary. Our main result
asserts…

Low Mach number limit of viscous compressible flows in the whole space

- MathematicsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 1999

This paper is devoted to the low Mach number limit of weak solutions to the compressible Navier–Stokes equations for isentropic fluids in the whole space Rd (d = 2 or 3). This problem was…

Weak solutions to the barotropic Navier–Stokes system with slip boundary conditions in time dependent domains

- Mathematics
- 2013

INCOMPRESSIBLE LIMIT FOR SOLUTIONS OF THE ISENTROPIC NAVIER–STOKES EQUATIONS WITH DIRICHLET BOUNDARY CONDITIONS

- Mathematics
- 1999

A BSTRACT . – We study here the limit of global weak solutions of the compressible Navier–Stokes equations (in the isentropic regime) in a bounded domain, with Dirichlet boundary conditions on the…

Incompressible Limit for Solutionsof the Isentropic Navier–Stokes Equationswith Dirichlet Boundary Conditions

- Mathematics
- 1999

Low Mach Number Flows in Time-Dependent Domains

- Mathematics, PhysicsSIAM J. Appl. Math.
- 2003

We perform a multiple time scale, single space scale analysis of a compressible fluid in a time-dependent domain, when the time variations of the boundary are small with respect to the acoustic…

Singular Limits in Thermodynamics of Viscous Fluids

- Mathematics, Physics
- 2009

In this series of lectures we discuss various aspects of the problems arising in scale analysis of the full Navier-Stokes-Fourier system. In particular, several simplied systems used in meteorology,…

Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit

- Materials Science
- 1981

Variable resistance control having wirewound resistance element with shorted end turns. A piece of metal secured to each end portion of an electrically nonconductive tape with a bonding material…