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Cascade of phases in turbulent flows

Christophe Cheverry (2006)

Bulletin de la Société Mathématique de France

This article is devoted to incompressible Euler equations (or to Navier-Stokes equations in the vanishing viscosity limit). It describes the propagation of quasi-singularities. The underlying phenomena are consistent with the notion of a cascade of energy.

Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid

Jaime H. Ortega, Lionel Rosier, Takéo Takahashi (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we investigate the motion of a rigid ball in an incompressible perfect fluid occupying 2 . We prove the global in time existence and the uniqueness of the classical solution for this fluid-structure problem. The proof relies mainly on weighted estimates for the vorticity associated with the strong solution of a fluid-structure problem obtained by incorporating some dissipation.

Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid

Jaime H. Ortega, Lionel Rosier, Takéo Takahashi (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we investigate the motion of a rigid ball in an incompressible perfect fluid occupying 2 . We prove the global in time existence and the uniqueness of the classical solution for this fluid-structure problem. The proof relies mainly on weighted estimates for the vorticity associated with the strong solution of a fluid-structure problem obtained by incorporating some dissipation.

Dissipation d’énergie pour des solutions faibles des équations d’Euler et Navier-Stokes incompressibles

Jean Duchon, Raoul Robert (1999/2000)

Séminaire Équations aux dérivées partielles

On étudie l’équation locale de l’énergie pour des solutions faibles des équations d’Euler et Navier-Stokes incompressibles tridimensionnelles. On explicite un terme de dissipation provenant de l’éventuel défaut de régularité de la solution. On donne au passage une preuve simple de la conjecture d’Onsager, améliorant un peu l’hypothèse de [1]. On propose une notion de solution dissipative pour de telles solutions faibles.

Existence of strong solutions for nonisothermal Korteweg system

Boris Haspot (2009)

Annales mathématiques Blaise Pascal

This work is devoted to the study of the initial boundary value problem for a general non isothermal model of capillary fluids derived by J. E Dunn and J. Serrin (1985) in [9, 16], which can be used as a phase transition model.We distinguish two cases, when the physical coefficients depend only on the density, and the general case. In the first case we can work in critical scaling spaces, and we prove global existence of solution and uniqueness for data close to a stable equilibrium. For general...

No production of entropy in the Euler fluid

R. F. Streater (2004)

Banach Center Publications

We derive the Euler equations as the hydrodynamic limit of a stochastic model of a hard-sphere gas. We show that the system does not produce entropy.

On blow-up of solution for Euler equations

Eric Behr, Jindřich Nečas, Hongyou Wu (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present numerical evidence for the blow-up of solution for the Euler equations. Our approximate solutions are Taylor polynomials in the time variable of an exact solution, and we believe that in terms of the exact solution, the blow-up will be rigorously proved.

On blow-up of solution for Euler equations

Eric Behr, Jindřich Nečas, Hongyou Wu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We present numerical evidence for the blow-up of solution for the Euler equations. Our approximate solutions are Taylor polynomials in the time variable of an exact solution, and we believe that in terms of the exact solution, the blow-up will be rigorously proved.

On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation

Georgios E. Zouraris (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We discretize the nonlinear Schrödinger equation, with Dirichlet boundary conditions, by a linearly implicit two-step finite element method which conserves the L 2 norm. We prove optimal order a priori error estimates in the L 2 and H 1 norms, under mild mesh conditions for two and three space dimensions.

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