Displaying similar documents to “About the decay of surface waves on viscous fluids without surface tension”

Asymptotic estimates for a perturbation of the linearization of an equation for compressible viscous fluid flow

Gerhard Ströhmer (2008)

Studia Mathematica

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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...

Numerical simulation of free-surface flows with surface tension

Sváček, Petr

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This paper focuses on the mathematical modelling and the numerical approximation of the flow of two immiscible incompressible fluids. The surface tension effects are taken into account and mixed boundary conditions are used. The weak formulation is introduced, discretized in time, and the finite element method is applied. The free surface motion is treated with the aid of the level set method. The numerical results are shown.

Global existence of solutions of the free boundary problem for the equations of magnetohydrodynamic compressible fluid

Piotr Kacprzyk (2005)

Banach Center Publications

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Global existence of solutions for equations describing a motion of magnetohydrodynamic compresible fluid in a domain bounded by a free surface is proved. In the exterior domain we have an electromagnetic field which is generated by some currents located on a fixed boundary. We have proved that the domain occupied by the fluid remains close to the initial domain for all time.

Stability and instability in nineteenth-century fluid mechanics

Olivier Darrigol (2002)

Revue d'histoire des mathématiques

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The stability or instability of a few basic flows was conjectured, debated, and sometimes proved in the nineteenth century. Motivations varied from turbulence observed in real flows to permanence expected in hydrodynamic theories of matter. Contemporary mathematics often failed to provide rigorous answers, and personal intuitions sometimes gave wrong results. Yet some of the basic ideas and methods of the modern theory of hydrodynamic instability occurred to the elite of British and...