Évolution d'une interface par capillarité et diffusion de volume. I. Existence locale en temps
Évolution d'une singularité de type cusp dans une poche de tourbillon
Évolution d'une singularité de type cusp dans une poche de tourbillon.
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...
Evolution in a migrating population model
We consider a model of migrating population occupying a compact domain Ω in the plane. We assume the Malthusian growth of the population at each point x ∈ Ω and that the mobility of individuals depends on x ∈ Ω. The evolution of the probability density u(x,t) that a randomly chosen individual occupies x ∈ Ω at time t is described by the nonlocal linear equation , where φ(x) is a given function characterizing the mobility of individuals living at x. We show that the asymptotic behaviour of u(x,t)...
Exact boundary controllability for higher order nonlinear Schrödinger equations with constant coefficients.
Exact boundary controllability of 3-D Euler equation
Exact boundary controllability of 3-D Euler equation
We prove the exact boundary controllability of the 3-D Euler equation of incompressible inviscid fluids on a regular connected bounded open set when the control operates on an open part of the boundary that meets any of the connected components of the boundary.
Exact boundary controllability of a nonlinear KdV equation with critical lengths
We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.
Exact boundary controllability of Galerkin's approximations of Navier-Stokes equations
Exact controllability in projections for three-dimensional Navier–Stokes equations
Exact propagators for soliton potentials.
Exact solutions and localized structures for higher-dimensional Burgers systems.
Exact solutions and symmetry operators for the nonlocal Gross-Pitaevskii equation with quadratic potential.
Exact solutions for a new fifth-order integrable system.
Exact solutions for a third-order KdV equation with variable coefficients and forcing term.
Exact solutions for equations of Bose-Fermi mixtures in one-dimensional optical lattice.
Exact solutions for the generalized BBM equation with variable coefficients.
Exact solutions of steady plane flows using -coordinates.
Exact solutions of steady plane MHD aligned flows using - or -coordinates.
Exact solutions of the generalized Benjamin-Bona-Mahony equation.