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1
Content available remote

About the decay of surface waves on viscous fluids without surface tension

100%
Ströhmer G.
Banach Center Publications
|
2003
|
tom 60
|
nr 1
55-72
EN
We study the decay of the motions of a viscous fluid subject to gravity without surface tension with a free boundary at the top. We show that the solutions of the linearization about the equilibrium state decay, but not exponentially in a uniform manner. We also discuss the consequences of this for the non-linear equations.
2
Content available remote

Stationary states and moving planes

100%
Ströhmer G.
Banach Center Publications
|
2008
|
tom 81
|
nr 1
501-513
EN
Most of the paper deals with the application of the moving plane method to different questions concerning stationary accumulations of isentropic gases. The first part compares the concepts of stationarity arising from the points of view of dynamics and the calculus of variations. Then certain stationary solutions are shown to be unstable. Finally, using the moving plane method, a short proof of the existence of energy-minimizing gas balls is given.
3
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Asymptotic estimates for a perturbation of the linearization of an equation for compressible viscous fluid flow

100%
Ströhmer G.
Studia Mathematica
|
2008
|
tom 185
|
nr 2
99-125
EN
We prove a priori estimates for a linear system of partial differential equations originating from the equations for the flow of a barotropic compressible viscous fluid under the influence of the gravity it generates. These estimates will be used in a forthcoming paper to prove the nonlinear stability of the motionless, spherically symmetric equilibrium states of barotropic, self-gravitating viscous fluids with respect to perturbations of zero total angular momentum. These equilibrium states as well as the non-stationary solutions occupy part of space, and a constant pressure is assumed on the free surface, but no surface tension.
4
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A remark about a Galerkin method

100%
Ströhmer G.
Banach Center Publications
|
1996
|
tom 33
|
nr 1
365-367
EN
It is shown that the approximating equations whose existence is required in the author's previous work on partially regular weak solutions can be constructed without any additional assumption about the equation itself. This leads to a variation of a Galerkin method.
5
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Existence and stability theorems for abstract parabolic equations, and some of their applications

64%
Ströhmer G., Zajączkowski W.
Banach Center Publications
|
1996
|
tom 33
|
nr 1
369-382
EN
For a class of semi-abstract evolution equations for sections on vector bundles on a three-dimensional compact manifold we prove that for initial values with certain symmetries strong solutions exist for all times. In case these solutions become small after some time, strong solutions exist also for small perturbations of these initial values. Many systems from fluid mechanics are included in this class.
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