Construction de solutions pour les équations de Korteweg-de Vries généralisées
Construction of axisymmetric steady states of an inviscid incompressible fluid by spatially discretized equations for pseudo-advected vorticity.
Control of the surface of a fluid by a wavemaker
The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.
Control of the surface of a fluid by a wavemaker
The control of the surface of water in a long canal by means of a wavemaker is investigated. The fluid motion is governed by the Korteweg-de Vries equation in Lagrangian coordinates. The null controllability of the elevation of the fluid surface is obtained thanks to a Carleman estimate and some weighted inequalities. The global uncontrollability is also established.
Control of underwater vehicles in inviscid fluids
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 incompressible Euler equations by a finite-dimensional external force
In this paper, we study the control system associated with the incompressible 3D Euler system. We show that the velocity field and pressure of the fluid are exactly controllable in projections by the same finite-dimensional control. Moreover, the velocity is approximately controllable. We also prove that 3D Euler system is not exactly controllable by a finite-dimensional external force.
Controllability of 3D low Reynolds number swimmers
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...
Creation and coupling of Rossby waves over topography and the breakdown of WKB theory
Damping of waves due to a soluble film.
Derivation and mathematical analysis of a nonlocal model for large amplitude internal waves
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.
Derivation and well-posedness of Boussinesq/Boussinesq systems for internal waves
We consider the propagation of internal waves at the interface between two layers of immiscrible fluids of different densities, under the rigid lid assumption, with the presence of surface tension and with uneven bottoms. We are interested in the case where the flow has a Boussinesq structure in both the upper and lower fluid domains. Following the global strategy introduced recently by Bona, Lannes and Saut [J. Math. Pures Appl. 89 (2008)], we derive an asymptotic model in this regime, namely the...
Determination of the Thickness and Composition Profiles for a Film of Binary Mixture on a Solid Substrate
We determine the steady-state structures that result from liquid-liquid demixing in a free surface film of binary liquid on a solid substrate. The considered model corresponds to the static limit of the diffuse interface theory describing the phase separation process for a binary liquid (model-H), when supplemented by boundary conditions at the free surface and taking the influence of the solid substrate into account. The resulting variational problem...
Development of a mathematical theory of inner gravitational waves in deep reservoirs of variable width.
Development of a particle interaction kernel function in MPS method for simulating incompressible free surface flow.
Dirichlet control of unsteady Navier–Stokes type system related to Soret convection by boundary penalty method
In this paper, we study the boundary penalty method for optimal control of unsteady Navier–Stokes type system that has been proposed as an alternative for Dirichlet boundary control. Existence and uniqueness of solutions are demonstrated and existence of optimal control for a class of optimal control problems is established. The asymptotic behavior of solution, with respect to the penalty parameter ϵ, is studied. In particular, we prove convergence of solutions of penalized control problem to the...
Dissipative Euler flows and Onsager's conjecture
Building upon the techniques introduced in [15], for any we construct periodic weak solutions of the incompressible Euler equations which dissipate the total kinetic energy and are Hölder-continuous with exponent . A famous conjecture of Onsager states the existence of such dissipative solutions with any Hölder exponent . Our theorem is the first result in this direction.
Distributed control of the generalized Korteweg-de Vries-Burgers equation.
Double bubbles minimize.
Doubly asymptotic trajectories of Lagrangian systems and a problem by Kirchhoff
We consider Lagrangian systems with Lagrange functions which exhibit a quadratic time dependence. We prove the existence of infinitely many solutions tending, as , to an «equilibrium at infinity». This result is applied to the Kirchhoff problem of a heavy rigid body moving through a boundless incompressible ideal fluid, which is at rest at infinity and has zero vorticity.
Dual integral equations -- revisited.