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Start Over Subject incompressible fluid

1. Analysis of the flows of incompressible fluids with pressure dependent viscosity fulfilling $\nu (p, \cdot ) \to + \infty $ as $p \to +\infty $

Creator:
Bulíček, M., Málek, Josef, and Rajagopal, Kumbakonam R.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
existence, weak solution, incompressible fluid, pressure-dependent viscosity, shear-dependent viscosity, and spatially periodic problem
Language:
English
Description:
Over a large range of the pressure, one cannot ignore the fact that the viscosity grows significantly (even exponentially) with increasing pressure. This paper concerns long-time and large-data existence results for a generalization of the Navier-Stokes fluid whose viscosity depends on the shear rate and the pressure. The novelty of this result stems from the fact that we allow the viscosity to be an unbounded function of pressure as it becomes infinite. In order to include a large class of viscosities and in order to explain the main idea in as simple a manner as possible, we restrict ourselves to a discussion of the spatially periodic problem.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On an evolutionary nonlinear fluid model in the limiting case

Creator:
Luckhaus, Stephan and Málek, Josef
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
shear-dependent viscosity, incompressible fluid, global-in-time existence, and weak solution
Language:
English
Description:
We consider the two-dimesional spatially periodic problem for an evolutionary system describing unsteady motions of the fluid with shear-dependent viscosity under general assumptions on the form of nonlinear stress tensors that includes those with pstructure. The global-in-time existence of a weak solution is established. Some models where the nonlinear operator corresponds to the case p = 1 are covered by this analysis.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. On the linear problem arising from motion of a fluid around a moving rigid body

Creator:
Nečasová, Šárka and Wolf, Jörg
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
incompressible fluid, rotating rigid body, and strong solution
Language:
English
Description:
We study a linear system of equations arising from fluid motion around a moving rigid body, where rotation is included. Originally, the coordinate system is attached to the fluid, which means that the domain is changing with respect to time. To get a problem in the fixed domain, the problem is rewritten in the coordinate system attached to the body. The aim of the present paper is the proof of the existence of a strong solution in a weighted Lebesgue space. In particular, we prove the existence of a global pressure gradient in L2.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid

Creator:
Cumsille, Patricio and Takahashi, Takéo
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Navier-Stokes equations, incompressible fluid, and rigid bodies
Language:
English
Description:
In this paper, we consider the interaction between a rigid body and an incompressible, homogeneous, viscous fluid. This fluid-solid system is assumed to fill the whole space $\Bbb R^d$, $d=2$ or $3$. The equations for the fluid are the classical Navier-Stokes equations whereas the motion of the rigid body is governed by the standard conservation laws of linear and angular momentum. The time variation of the fluid domain (due to the motion of the rigid body) is not known {\it a priori}, so we deal with a free boundary value problem. \endgraf We improve the known results by proving a complete wellposedness result: our main result yields a local in time existence and uniqueness of strong solutions for $d=2$ or $3$. Moreover, we prove that the solution is global in time for $d=2$ and also for $d=3$ if the data are small enough.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public