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On the Cauchy Problem for the Pressureless Euler–Navier–Stokes System in the Whole Space
Springer Science and Business Media LLC - Tập 23 - Trang 1-16 - 2021
Young-Pil Choi, Jinwook Jung
In this paper, we study the global Cauchy problem for a two-phase fluid model consisting of the pressureless Euler equations and the incompressible Navier–Stokes equations where the coupling of two equations is through the drag force. We establish the global-in-time existence and uniqueness of classical solutions for that system when the initial data are sufficiently small and regular. Main diffic... hiện toàn bộ
$$L^q$$ -Solution of the Robin Problem for the Stokes System with Coriolis Force
Springer Science and Business Media LLC - Tập 20 - Trang 1589-1616 - 2018
Dagmar Medková
We define single layer potential and double layer potential for the stationary Stokes system with Coriolis term and study properties of these potentials. Then using the integral equation method we study the Dirichlet problem, the Neumann problem and the Robin problem for the Stokes system with Coriolis term. We look for solutions of the problems such that the maximal functions of the velocity $$\m... hiện toàn bộ
Spectral Element Discretization of the Circular Driven Cavity. Part III: The Stokes Equations in Primitive Variables
Springer Science and Business Media LLC - Tập 5 - Trang 24-69 - 2003
Z. Belhachmi, C. Bernardi, A. Karageorghis
This paper deals with the spectral element discretization of the Stokes equations in a disk with discontinuous boundary data. The numerical treatment does not involve any regularization of these data. Based on a variational formulation in the primitive variables of velocity and pressure, we describe a discretization of the Stokes problem and derive error estimates in Sobolev spaces with appropriat... hiện toàn bộ
Well-Posedness of a Gas—Solid Phase Transition Problem
Springer Science and Business Media LLC - Tập 1 - Trang 282-308 - 1999
I. A. Kaliev, A. V. Kazhikhov
A new model for liquid—solid phase transitions within the frame of complete Navier—Stokes equations in a liquid phase is proposed. It takes into account such properties of liquid as compressibility, viscosity, and heat conductivity. The local existence and uniqueness of a smooth solution to the related initial-boundary value problem is proved.
On Two-Dimensional Magnetic Bénard Problem with Mixed Partial Viscosity
Springer Science and Business Media LLC - Tập 17 - Trang 769-797 - 2015
Jianfeng Cheng, Lili Du
In this paper, we deal with the Cauchy problem of the two-dimensional magnetic Bénard problem with mixed partial viscosity. More precisely, the global well-posedness of 2D magnetic Bénard problem without thermal diffusivity and with vertical or horizontal magnetic diffusion is obtained. Moreover, the global regularity and some conditional regularity of strong solutions are obtained for 2D magnetic... hiện toàn bộ
The 3-D Inviscid Limit Result Under Slip Boundary Conditions. A Negative Answer
Springer Science and Business Media LLC - Tập 14 - Trang 55-59 - 2011
H. Beirão da Veiga, F. Crispo
We show that, in general, the solutions to the initial-boundary value problem for the Navier-Stokes equations under a widely adopted Navier-type slip boundary condition do not converge, as the viscosity goes to zero, to the solution of the Euler equations under the classical zero-flux boundary condition, and same smooth initial data, in any arbitrarily small neighborhood of the initial time. Conve... hiện toàn bộ
On the Singular Incompressible Limit of Inviscid Compressible Fluids
Springer Science and Business Media LLC - Tập 2 - Trang 107-125 - 2000
P. Secchi
We consider the Euler equations of barotropic inviscid compressible fluids in a bounded domain. It is well known that, as the Mach number goes to zero, the compressible flows approximate the solution of the equations of motion of inviscid, incompressible fluids. In this paper we discuss, for the boundary case, the different kinds of convergence under various assumptions on the data, in particular ... hiện toàn bộ
A Note on Liouville Theorem for Stationary Flows of Shear Thickening Fluids in the Plane
Springer Science and Business Media LLC - Tập 15 - Trang 771-782 - 2013
Guo Zhang
In this paper we consider the entire weak solutions of the equations for stationary flows of shear thickening fluids in the plane and prove Liouville theorem under the global boundedness condition of velocity fields.
Spectral Element Discretization of the Circular Driven Cavity. Part IV: The Navier-Stokes Equations
Springer Science and Business Media LLC - Tập 6 - Trang 121-156 - 2004
Zakaria Belhachmi, Christine Bernardi, Andreas Karageorghis
This paper deals with the spectral element discretization of the Navier-Stokes equations in a disk with discontinuous boundary data, which is known as the driven cavity problem. The numerical treatment does not involve any regularization of these data. Relying on a variational formulation in the primitive variables of velocity and pressure, we describe a discretization of these equations and deriv... hiện toàn bộ
A Remark on the Existence of 2-D Steady Navier–Stokes Flow in Bounded Symmetric Domain Under General Outflow Condition
Springer Science and Business Media LLC - - 2007
Hiroko Morimoto
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