$$L^q$$ -Solution of the Robin Problem for the Stokes System with Coriolis ForceSpringer 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
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Spectral Element Discretization of the Circular Driven Cavity. Part III: The Stokes Equations in Primitive VariablesSpringer 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 appropr...... hiện toàn bộ
Well-Posedness of a Gas—Solid Phase Transition ProblemSpringer 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.
The 3-D Inviscid Limit Result Under Slip Boundary Conditions. A Negative AnswerSpringer 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
Spectral Element Discretization of the Circular Driven Cavity. Part IV: The Navier-Stokes EquationsSpringer 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
de...... hiện toàn bộ
Unstable Eigenvalues Associated with Inviscid Fluid FlowsSpringer Science and Business Media LLC - - 2000
S. Friedlander, M. Vishik, V. Yudovich
An example is presented of a class of periodic, two-dimensional, inviscid fluid flows where the stability spectrum contains both discrete unstable eigenvalues and an unstable essential spectrum. The method of averaging is used to demonstrate the existence of unstable eigenvalues. For such flows spectral instability implies nonlinear instability.