All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 94 Next

Displaying 1861 – 1880 of 3487

Showing per page

On local motion of a compressible barotropic viscous fluid bounded by a free surface

W. Zajączkowski (1992)

Banach Center Publications

We consider the motion of a viscous compressible barotropic fluid in ℝ³ bounded by a free surface which is under constant exterior pressure, both with surface tension and without it. In the first case we prove local existence of solutions in anisotropic Hilbert spaces with noninteger derivatives. In the case without surface tension the anisotropic Sobolev spaces with integration exponent p > 3 are used to omit the coefficients which are increasing functions of 1/T, where T is the existence time....

On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids

Piotr Boguslaw Mucha, Wojciech Zajączkowski (2002)

Annales Polonici Mathematici

The local existence of solutions for the compressible Navier-Stokes equations with the Dirichlet boundary conditions in the L p -framework is proved. Next an almost-global-in-time existence of small solutions is shown. The considerations are made in Lagrangian coordinates. The result is sharp in the L p -approach, because the velocity belongs to W r 2 , 1 with r > 3.

On measure solutions to the Zero-pressure gas model and their uniqueness

Jiequan Li, Gerald G. Warnecke (2002)

Mathematica Bohemica

The system of zero-pressure gas dynamics conservation laws describes the dynamics of free particles sticking under collision while mass and momentum are conserved. The existence of such solutions was established some time ago. Here we report a uniqueness result that uses the Oleinik entropy condition and a cohesion condition. Both of these conditions are automatically satisfied by solutions obtained in previous existence results. Important tools in the proof of uniqueness are regularizations, generalized...

On modeling flow between adjacent surfaces where the fluid is governed by implicit algebraic constitutive relations

Andreas Almqvist, Evgeniya Burtseva, Kumbakonam R. Rajagopal, Peter Wall (2024)

Applications of Mathematics

We consider pressure-driven flow between adjacent surfaces, where the fluid is assumed to have constant density. The main novelty lies in using implicit algebraic constitutive relations to describe the fluid's response to external stimuli, enabling the modeling of fluids whose responses cannot be accurately captured by conventional methods. When the implicit algebraic constitutive relations cannot be solved for the Cauchy stress in terms of the symmetric part of the velocity gradient, the traditional...

On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations

Xuejun Xu, C. O. Chow, S. H. Lui (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.

On nonoverlapping domain decomposition methods for the incompressible Navier-Stokes equations

Xuejun Xu, C. O. Chow, S. H. Lui (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, a Dirichlet-Neumann substructuring domain decomposition method is presented for a finite element approximation to the nonlinear Navier-Stokes equations. It is shown that the Dirichlet-Neumann domain decomposition sequence converges geometrically to the true solution provided the Reynolds number is sufficiently small. In this method, subdomain problems are linear. Other version where the subdomain problems are linear Stokes problems is also presented.

On nonstationary motion of a fixed mass of a general fluid bounded by a free surface

Ewa Zadrzyńska, Wojciech M. Zajączkowski (2003)

Banach Center Publications

In the paper the motion of a fixed mass of a viscous compressible heat conducting fluid is considered. Assuming that the initial data are sufficiently close to an equilibrium state and the external force, the heat sources and the heat flow through the boundary vanish, we prove the existence of a global in time solution which is close to the equilibrium state for any moment of time.

On nonstationary motion of a fixed mass of a general viscous compressible heat conducting capillary fluid bounded by a free boundary

Ewa Zadrzyńska (1999)

Applicationes Mathematicae

The motion of a fixed mass of a viscous compressible heat conducting capillary fluid is examined. Assuming that the initial data are sufficiently close to a constant state and the external force vanishes we prove the existence of a global-in-time solution which is close to the constant state for any moment of time. Moreover, we present an analogous result for the case of a barotropic viscous compressible fluid.

Currently displaying 1861 – 1880 of 3487