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We study the linearized water-wave problem in a bounded domain (e.g.a finite pond of water) of , having a cuspidal boundary irregularity created by a submerged body. In earlier publications the authors discovered that in this situation the spectrum of the problem may contain a continuous component in spite of the boundedness of the domain. Here, we proceed to impose and study radiation conditions at a point of the water surface, where a submerged body touches the surface (see Fig. 1). The radiation...
We study the linearized water-wave problem in a bounded domain (e.g. a
finite pond of water) of , having a cuspidal boundary
irregularity created by a submerged body. In earlier publications the
authors discovered that
in this situation the spectrum of the problem may contain a
continuous component in spite of the boundedness of the domain.
Here, we proceed to impose and study radiation conditions at a point
of the water surface, where
a submerged body touches the surface
(see Fig. 1)....
Nous prouvons que pour toute solution du problème de Kelvin–Helmholtz des nappes de tourbillons pour l’équation d’Euler bi-dimensionnelle, définie localement en temps, la courbe de saut de et la densité de tourbillon sont analytiques (sous une hypothèse de régularité Holderienne de la courbe de saut). Nous donnons également un résultat de régularité partielle de la trace de sur lorsque est définie sur un demi-interval .
Nous prouvons que pour toute solution u du problème
de Kelvin–Helmholtz des nappes de tourbillons pour
l'équation d'Euler bi-dimensionnelle, définie localement en
temps,
la courbe de saut de u et la densité de tourbillon sont
analytiques (sous une hypothèse de régularité Holderienne
de la courbe de saut).
Nous donnons également un résultat de régularité partielle
de la trace de u sur t=0 lorsque u est définie sur un
demi-interval [O,T[.
We review some recent results for a class of fluid mechanics equations called active
scalars, with fractional dissipation. Our main examples are the surface quasi-geostrophic
equation, the Burgers equation, and the Cordoba-Cordoba-Fontelos model. We discuss
nonlocal maximum principle methods which allow to prove existence of global regular
solutions for the critical dissipation. We also recall what is known about the possibility
of finite time blow...
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.
La compréhension du passage des équations de la mécanique des fluides compressibles aux équations incompressibles a fait de grands progrès ces vingt dernières années. L’objectif de cet exposé est de présenter l’évolution des méthodes mathématiques mises en œuvre pour étudier ce passage à la limite, depuis les travaux de S. Klainerman et A. Majda dans les années quatre–vingts, jusqu’à ceux récents de G. Métivier et S. Schochet (pour les équations non isentropiques). Suivant les conditions initiales...
In this paper, we study the long wave approximation for quasilinear
symmetric hyperbolic systems. Using the technics developed by
Joly-Métivier-Rauch for nonlinear geometrical optics, we prove that
under suitable assumptions the long wave limit is described by
KdV-type systems. The error estimate if the system is coupled appears to
be better. We apply formally our technics to Euler equations with free
surface and Euler-Poisson systems. This leads to new systems of KdV-type.
The flow trough the Strait of Gibraltar could be analyzed as a problem of
two-layer
hydraulic exchange between the Atlantic ocean and the Mediterranean sea. The
shallow water
equations in both layers coupled together are an important tool to simulate this
phenomenon. In
this paper we perform an upwind schemes for hyperbolic equations based on the
Roe approximate
Riemann solver, to study the resulting model. The main goal assigned was to
predict the location
of the interface between the two layers....
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