The Cauchy-Poisson waves in an inviscid rotating stratified liquid.
The dock problem revisited.
The dual integral equation method in hydromechanical systems.
The Eulerian limit and the slip boundary conditions-admissible irregularity of the boundary
We investigate the inviscid limit for the stationary Navier-Stokes equations in a two dimensional bounded domain with slip boundary conditions admitting nontrivial inflow across the boundary. We analyze admissible regularity of the boundary necessary to obtain convergence to a solution of the Euler system. The main result says that the boundary of the domain must be at least C²-piecewise smooth with possible interior angles between regular components less than π.
The evolution Darcy-Boussinesq system (a weak maximum principle and the uniqueness)
The existence of global solutions to the elliptic-hyperbolic Davey-Stewartson system with small initial data
The four positive vortices problem : regions of chaotic behavior and the non-integrability
The hodograph method for convex profiles
The large deformation of nonlinearly elastic shells in axisymmetric flows
The limiting amplitude principle applied to the motion of floating bodies
The modulational regime of three-dimensional water waves and the Davey-Stewartson system
The motion of the free surface of a liquid
The nappe profile of a free overfall
The phenomenon of the free overfall at the sharp drop of a channel bed has been deeply investigated experimentally since the pioneering work of Rouse (1933). Its behaviour is well known at least in the usual case of a wide rectangular channel. However, no complete theoretical solution has yet been obtained. Assuming the steady flow to be two-dimensional, irrotational and frictionless, an analytical solution for the flow field is obtained accounting for the presence of two free boundaries. By applying...
The optimum shape of an hydrofoil with no cavitation
The shallow water equations: Conservation laws and symplectic geometry.
The Singularity Expansion Method applied to the transient motions of a floating elastic plate
In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles...
The vortex method for 2D ideal flows in the exterior of a disk
The vortex method is a common numerical and theoretical approach used to implement the motion of an ideal flow, in which the vorticity is approximated by a sum of point vortices, so that the Euler equations read as a system of ordinary differential equations. Such a method is well justified in the full plane, thanks to the explicit representation formulas of Biot and Savart. In an exterior domain, we also replace the impermeable boundary by a collection of point vortices generating the circulation...
Theoretical and numerical aspects of stochastic nonlinear Schrödinger equations
We describe several results obtained recently on stochastic nonlinear Schrödinger equations. We show that under suitable smoothness assumptions on the noise, the nonlinear Schrödinger perturbed by an additive or multiplicative noise is well posed under similar assumptions on the nonlinear term as in the deterministic theory. Then, we restrict our attention to the case of a focusing nonlinearity with critical or supercritical exponent. If the noise is additive, smooth in space and non degenerate,...
Three dimensional Green's function for ship motion at forward speed.
Three-dimensional Korteweg-de Vries equation and traveling wave solutions.