scholarly journals Self-propelled motion of a rigid body inside a density dependent incompressible fluid

2020 ◽  
Author(s):  
Sarka Necasova ◽  
Mythily Ramaswamy ◽  
Arnab Roy ◽  
Anja Schlomerkemper
Keyword(s):  
Angular Momentum ◽  
Weak Solution ◽  
Global Existence ◽  
Viscous Fluid ◽  
Rigid Body ◽  
Incompressible Fluid ◽  
Stokes System ◽  
Navier Stokes ◽  
Navier Condition ◽  
Whole Space

This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole space. The fluid is modelled by the incompressible nonhomogeneous Navier-Stokes system with a nonnegative density. The motion of the rigid body is described by the  balance of linear and angular momentum. We consider the case where slip is allowed at the fluid-solid interface through Navier condition and prove the global existence of a weak solution.

scholarly journals Global existence for a two-species chemotaxis-Navier-Stokes system with $ p $-Laplacian

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jiayi Han ◽  
Changchun Liu
Keyword(s):  
Weak Solution ◽  
Global Existence ◽  
Stokes System ◽  
Three Dimensional ◽  
Global Weak Solution ◽  
Navier Stokes ◽  
Bounded Domains

<p style='text-indent:20px;'>We consider a two-species chemotaxis-Navier-Stokes system with <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>-Laplacian in three-dimensional smooth bounded domains. It is proved that for any <inline-formula><tex-math id="M3">\begin{document}$ p\geq2 $\end{document}</tex-math></inline-formula>, the problem admits a global weak solution.</p>

ON THE ROBIN PROBLEM FOR STOKES AND NAVIER–STOKES SYSTEMS

2006 ◽  
Vol 16 (05) ◽  
pp. 701-716 ◽  
Author(s):  
REMIGIO RUSSO ◽  
ALFONSINA TARTAGLIONE
Keyword(s):  
Boundary Layer ◽  
Weak Solution ◽  
Lipschitz Domain ◽  
Stokes System ◽  
Navier Stokes ◽  
Robin Problem ◽  
Layer Potentials ◽  
Very Weak Solution ◽  
Stokes Systems ◽  
Compact Boundary

The Robin problem for Stokes and Navier–Stokes systems is considered in a Lipschitz domain with a compact boundary. By making use of the boundary layer potentials approach, it is proved that for Stokes system this problem admits a very weak solution under suitable assumptions on the boundary datum. A similar result is proved for the Navier–Stokes system, provided that the datum is "sufficiently small".

FLOWS OF VISCOUS COMPRESSIBLE FLUIDS UNDER STRONG STRATIFICATION: INCOMPRESSIBLE LIMITS FOR LONG-RANGE POTENTIAL FORCES

2011 ◽  
Vol 21 (01) ◽  
pp. 7-27 ◽  
Author(s):  
EDUARD FEIREISL
Keyword(s):  
Mach Number ◽  
Acoustic Waves ◽  
Stokes System ◽  
Hybrid Methods ◽  
Singular Limit ◽  
Acoustic Energy ◽  
Compressible Fluids ◽  
Navier Stokes ◽  
Whole Space ◽  
Rage Theorem

We study the singular limit of the compressible Navier–Stokes system in the whole space ℝ3, where the Mach number and Froude number are proportional to a small parameter ε → 0. The central issue is the local decay of the acoustic energy proved by means of the RAGE theorem. The result is quite general and the proposed approach can be applied to a large variety of problems that concern propagation of acoustic waves in compressible fluids. In particular, the method can be used for showing stability of various numerical schemes based on the so-called hybrid methods.

Singular limit of a dispersive Navier–Stokes system with an entropy structure

2014 ◽  
Vol 13 (01) ◽  
pp. 77-99
Author(s):  
C. David Levermore ◽  
Weiran Sun ◽  
Konstantina Trivisa
Keyword(s):  
Stokes System ◽  
Singular Limit ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Third Order ◽  
Fluid System ◽  
Low Mach Number ◽  
Low Mach Number Limit ◽  
Whole Space ◽  
Entropy Structure

We prove a low Mach number limit for a dispersive fluid system [3] which contains third-order corrections to the compressible Navier–Stokes. We show that the classical solutions to this system in the whole space ℝn converge to classical solutions to ghost-effect systems [7]. Our analysis follows the framework in [4], which is built on the methodology developed by Métivier and Schochet [6] and Alazard [1] for systems up to the second order. The key new ingredient is the application of the entropy structure of the dispersive fluid system. This structure enables us to treat cases not covered in [4] and to simplify the analysis in [4].

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