On the existence of hydrodynamic motion in a domain with free boundary type conditions

Mulone, G.; Salemi, F.

doi:10.1007/bf02128580

Cited by 18 publications

(6 citation statements)

References 11 publications

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“…They were also used in [14] for the study of the non stationary Navier-Stokes equations in half-spaces of R 3 . We finally refer to [43,44] for the study of the non stationary problem of Navier-Stokes with mixed boundary conditions that include (1.5) without friction.…”

Section: Introductionmentioning

confidence: 99%

Weighted Hilbert spaces for the stationary exterior Stokes problem with Navier slip boundary conditions

Dhifaoui

Meslameni

Razafison

2019

Journal of Mathematical Analysis and Applications

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In this paper, we analyse the three-dimensional exterior Stokes problem with the Navier slip boundary conditions, describing the flow of a viscous and incompressible fluid past an obstacle where it is assumed that the fluid may slip at the boundary. Because the flow domain is unbounded, we set the problem in weighted spaces in order to control the behavior at infinity of the solutions. This functional framework also allows to prescribe various behaviors at infinity of the solutions (growth or decay). Existence and uniqueness of solutions are shown in a Hilbert setting which gives the tools for a possible numerical analysis of the problem. Weighted Korn's inequalities are the key point in order to study the variational problem.

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Section: Introductionmentioning

confidence: 99%

Weighted Hilbert spaces for the stationary exterior Stokes problem with Navier slip boundary conditions

Dhifaoui

Meslameni

Razafison

2019

Journal of Mathematical Analysis and Applications

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“…. Then, we apply the Sobolev inequality and the generalised Poincaré inequality (see [17] or Lemma 2.1 in [18])…”

Section: The Euler-lagrange Equations For the Nonlinear Stability Ana...mentioning

confidence: 99%

The energy method analysis of the Darcy–Bénard problem with viscous dissipation

Barletta

Mulone

2020

Continuum Mech. Thermodyn.

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A nonlinear analysis of the effect of viscous dissipation on the Rayleigh-Bénard instability in a fluid saturated porous layer is performed. The saturated medium is modelled through Darcy's law, with the layer bounded by two parallel impermeable walls kept at different uniform temperatures, so that heating from below is supplied. While it is well known that viscous dissipation does not influence the linear threshold to instability, a rigorous nonlinear analysis of the instability when viscous dissipation is taken into account is still lacking. This paper aims to fill this gap. The energy method is employed to prove the nonlinear conditional stability of the basic conduction state. In other words, it is shown that a finite initial perturbation exponentially decays in time provided that its initial amplitude is smaller than a given finite value.

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“…Early in 1973, V. Solonnikov and V. Ščailov [30] gave the first rigorous mathematical analysis to Navier-Stokes equations with Navier-slip boundary conditions, they focused on linear stationary equations in 3D with the coefficient k(x) = 0 and the external force f ∈ L 2 . In 1980s, G. Mulone and F. Salemi [24,25] considered the Navier-Stokes equations with Navier-slip boundary conditions in a three dimensional bounded domain. They proved the well-posedness for the corresponding stationary problem, and the existence of weak solution for the evolutionary problem.…”

Section: 8)mentioning

confidence: 99%

Rayleigh–Taylor instability for nonhomogeneous incompressible fluids with Navier‐slip boundary conditions

Ding

2020

Math Methods in App Sciences

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This paper is concerned with the Rayleigh-Taylor instability for the nonhomogeneous incompressible Navier-Stokes equations with Navier-slip boundary conditions around a steady-state in an infinite slab, where the Navier-slip coefficients do not have defined sign and the slab is horizontally periodic. Motivated by [18], we extend the result from Dirichlet boundary condition to Navier-slip boundary conditions. Our results indicate the factor that "heavier density with increasing height" still plays a key role in the instability under Navier-slip boundary conditions.

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On the existence of hydrodynamic motion in a domain with free boundary type conditions

Cited by 18 publications

References 11 publications

Weighted Hilbert spaces for the stationary exterior Stokes problem with Navier slip boundary conditions

Weighted Hilbert spaces for the stationary exterior Stokes problem with Navier slip boundary conditions

The energy method analysis of the Darcy–Bénard problem with viscous dissipation

Rayleigh–Taylor instability for nonhomogeneous incompressible fluids with Navier‐slip boundary conditions

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