Page 1 Next

Displaying 1 – 20 of 43

Showing per page

Air entrainment in transient flows in closed water pipes : A two-layer approach

C. Bourdarias, M. Ersoy, Stéphane Gerbi (2013)

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

In this paper, we first construct a model for free surface flows that takes into account the air entrainment by a system of four partial differential equations. We derive it by taking averaged values of gas and fluid velocities on the cross surface flow in the Euler equations (incompressible for the fluid and compressible for the gas). The obtained system is conditionally hyperbolic. Then, we propose a mathematical kinetic interpretation of this system to finally construct a two-layer kinetic scheme...

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.

Control of underwater vehicles in inviscid fluids

Rodrigo Lecaros, Lionel Rosier (2014)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we investigate the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid whose flow is assumed to be irrotational. Taking as control input the flow of the fluid through a part of the boundary of the rigid body, we obtain a finite-dimensional system similar to Kirchhoff laws in which the control input appears through both linear terms (with time derivative) and bilinear terms. Applying Coron’s return method, we establish some local controllability...

Controllability of 3D low Reynolds number swimmers

Jérôme Lohéac, Alexandre Munnier (2014)

ESAIM: Control, Optimisation and Calculus of Variations

In this article, we consider a swimmer (i.e. a self-deformable body) immersed in a fluid, the flow of which is governed by the stationary Stokes equations. This model is relevant for studying the locomotion of microorganisms or micro robots for which the inertia effects can be neglected. Our first main contribution is to prove that any such microswimmer has the ability to track, by performing a sequence of shape changes, any given trajectory in the fluid. We show that, in addition, this can be done...

Derivation and mathematical analysis of a nonlocal model for large amplitude internal waves

David Lannes (2008/2009)

Séminaire Équations aux dérivées partielles

This note is devoted to the study of a bi-fluid generalization of the nonlinear shallow-water equations. It describes the evolution of the interface between two fluids of different densities. In the case of a two-dimensional interface, this systems contains unexpected nonlocal terms (that are of course not present in the usual one-fluid shallow water equations). We show here how to derive this systems from the two-fluid Euler equations and then show that it is locally well-posed.

Dissipative Euler flows and Onsager's conjecture

Camillo De Lellis, László Székelyhidi (2014)

Journal of the European Mathematical Society

Building upon the techniques introduced in [15], for any θ < 1 10 we construct periodic weak solutions of the incompressible Euler equations which dissipate the total kinetic energy and are Hölder-continuous with exponent θ . A famous conjecture of Onsager states the existence of such dissipative solutions with any Hölder exponent θ < 1 3 . Our theorem is the first result in this direction.

Ekman boundary layers in rotating fluids

Jean-Yves Chemin, Benoît Desjardins, Isabelle Gallagher, Emmanuel Grenier (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general L 2 initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.

Ekman boundary layers in rotating fluids

Jean-Yves Chemin, Benoît Desjardins, Isabelle Gallagher, Emmanuel Grenier (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general L2 initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.

Évolution de tourbillon à support compact

Dragoş Iftimie (1999)

Journées équations aux dérivées partielles

On considère l’équation d’Euler incompressible dans le plan. Dans le cas où le tourbillon est positif et à support compact on montre que le support du tourbillon croît au plus comme O [ ( t log t ) ] 1 / 4 , améliorant la borne O ( t 1 / 3 ) obtenue par C. Marchioro. Dans le cas où le tourbillon change de signe, on donne un exemple de tourbillon initial tel que la croissance du diamètre du support du tourbillon est exactement O ( t ) . Enfin, dans le cas du demi-plan et du tourbillon initial positif et à support compact, on montre que le...

Évolution d'une singularité de type cusp dans une poche de tourbillon.

Raphaël Danchin (2000)

Revista Matemática Iberoamericana

We investigate the evolution of singularities in the boundary of a vortex patch for two-dimensional incompressible Euler equations. We are particularly interested in cusp-like singularities which, according to numerical simulations, are stable. In this paper, we first prove that, unlike the case of a corner-like singularity, the cusp-like singularity generates a lipschitzian velocity. We then state a global result of persistence of conormal regularity with respect to vector fields vanishing at a...

Currently displaying 1 – 20 of 43

Page 1 Next