scholarly journals Solvability of the problem of the self-propelled motion of several rigid bodies in a viscous incompressible fluid

2007 ◽  
Vol 53 (3-4) ◽  
pp. 413-435 ◽  
Author(s):  
Victor N. Starovoitov
Keyword(s):  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Rigid Bodies ◽  
The Self

Embeddings for the space on sets of finite perimeter

2019 ◽  
Vol 150 (5) ◽  
pp. 2442-2461 ◽  
Author(s):  
Nikolai V. Chemetov ◽  
Anna L. Mazzucato
Keyword(s):  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Rigid Bodies ◽  
Deformation Tensor ◽  
Integrable Deformation ◽  
Sets Of Finite Perimeter ◽  
Open Set ◽  
Finite Perimeter ◽  
Continuous Embedding

AbstractGiven an open set with finite perimeter $\Omega \subset {\open R}^n$, we consider the space $LD_\gamma ^{p}(\Omega )$, $1\les p<\infty $, of functions with pth-integrable deformation tensor on Ω and with pth-integrable trace value on the essential boundary of Ω. We establish the continuous embedding $LD_\gamma ^{p}(\Omega )\subset L^{pN/(N-1)}(\Omega )$. The space $LD_\gamma ^{p}(\Omega )$ and this embedding arise naturally in studying the motion of rigid bodies in a viscous, incompressible fluid.

scholarly journals On the reconstruction of obstacles and of rigid bodies immersed in a viscous incompressible fluid

2017 ◽  
Vol 25 (1) ◽  
pp. 1-21
Author(s):  
Jorge San Martín ◽  
Erica L. Schwindt ◽  
Takéo Takahashi
Keyword(s):  
Incompressible Fluid ◽  
Stokes System ◽  
Partial Information ◽  
Viscous Incompressible Fluid ◽  
Rigid Bodies ◽  
Navier Stokes ◽  
Fluid Structure ◽  
Structure System ◽  
Spherical Waves ◽  
Enclosure Method

AbstractWe consider the geometrical inverse problem consisting in recovering an unknown obstacle in a viscous incompressible fluid by measurements of the Cauchy force on the exterior boundary. We deal with the case where the fluid equations are the nonstationary Stokes system and using the enclosure method, we can recover the convex hull of the obstacle and the distance from a point to the obstacle. With the same method, we can obtain the same result in the case of a linear fluid-structure system composed by a rigid body and a viscous incompressible fluid. We also tackle the corresponding nonlinear systems: the Navier–Stokes system and a fluid-structure system with free boundary. Using complex spherical waves, we obtain some partial information on the distance from a point to the obstacle.

Slender-body theory for slow viscous flow

1976 ◽  
Vol 75 (4) ◽  
pp. 705-714 ◽  
Author(s):  
Joseph B. Keller ◽  
Sol I. Rubinow
Keyword(s):  
Integral Equation ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Unit Length ◽  
The Body ◽  
Slender Body ◽  
Slow Flow ◽  
Slender Body Theory ◽  
Slow Viscous Flow ◽  
Body Theory

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.

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