Displaying similar documents to “Global calibrations for the non-homogeneous Mumford-Shah functional”

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.

The inviscid limit for density-dependent incompressible fluids

Raphaël Danchin (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

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This paper is devoted to the study of smooth flows of density-dependent fluids in ℝ N or in the torus 𝕋 N . We aim at extending several classical results for the standard Euler or Navier-Stokes equations, to this new framework. Existence and uniqueness is stated on a time interval independent of the viscosity μ when μ goes to 0 . A blow-up criterion involving the norm of vorticity in L 1 ( 0 , T ; L ∞ ) is also proved. Besides, we show that if the density-dependent Euler equations have a smooth...

Halfway to a solution of X 2 - D Y 2 = - 3

R. A. Mollin, A. J. Van der Poorten, H. C. Williams (1994)

Journal de théorie des nombres de Bordeaux

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It is well known that the continued fraction expansion of D readily displays the midpoint of the principal cycle of ideals, that is, the point halfway to a solution of x 2 - D y 2 = ± 1 . Here we notice that, analogously, the point halfway to a solution of x 2 - D y 2 = - 3 can be recognised. We explain what is going on.