The inviscid limit for density-dependent incompressible fluids

Raphaël Danchin

Displaying similar documents to “The inviscid limit for density-dependent incompressible fluids”

Incompressible, inviscid limit of the compressible Navier–Stokes system

Nader Masmoudi (2001)

Annales de l'I.H.P. Analyse non linéaire

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On a free boundary barotropic model

P.-L. Lions, N. Masmoudi (1999)

Annales de l'I.H.P. Analyse non linéaire

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Global calibrations for the non-homogeneous Mumford-Shah functional

Massimiliano Morini (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Using a calibration method we prove that, if $Γ \subset Ω$ is a closed regular hypersurface and if the function $g$ is discontinuous along $Γ$ and regular outside, then the function $u_{β}$ which solves $\{\begin{matrix} Δ u_{β} = β (u_{β} - g) & in Ω ∖ Γ \\ \partial_{ν} u_{β} = 0 & on \partial Ω \cup Γ \end{matrix}$ is in turn discontinuous along $Γ$ and it is the unique absolute minimizer of the non-homogeneous Mumford-Shah functional $\int_{Ω ∖ S_{u}} {| \nabla u |}^{2} d x + ℋ^{n - 1} (S_{u}) + β \int_{Ω ∖ S_{u}} {(u - g)}^{2} d x,$ over $S B V (Ω)$ , for $β$ large enough. Applications of the result to the study of the gradient flow by the method of minimizing movements are shown. ...

On the regularity of the bilinear term for solutions to the incompressible Navier-Stokes equations.

Marco Cannone, Fabrice Planchon (2000)

Revista Matemática Iberoamericana

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We derive various estimates for strong solutions to the Navier-Stokes equations in C([0,T),L(R)) that allow us to prove some regularity results on the kinematic bilinear term.

Asymptotic behavior of global solutions to the Navier-Stokes equations in R.

Fabrice Planchon (1998)

Revista Matemática Iberoamericana

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We construct global solutions to the Navier-Stokes equations with initial data small in a Besov space. Under additional assumptions, we show that they behave asymptotically like self-similar solutions.

Remarks on the equatorial shallow water system

Chloé Mullaert (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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This article recalls the results given by A. Dutrifoy, A. Majda and S. Schochet in [1] in which they prove an uniform estimate of the system as well as the convergence to a global solution of the long wave equations as the Froud number tends to zero. Then, we will prove the convergence with weaker hypothesis and show that the life span of the solutions tends to infinity as the Froud number tends to zero.