On the existence and the regularity of an initial boundary problem of vorticity equation
On the Existence and Uniqueness of Non-homogeneous Motions in Exterior Domains.
On the Exterior Capillarity Problem.
On the global existence for the Muskat problem
The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an maximum principle, in the form of a new “log” conservation law which is satisfied by the equation (1) for the interface. Our second result is a proof of global existence for unique strong solutions if the initial data is smaller than an explicitly computable constant, for instance . Previous results of this...
On the global well-posedness of the Boussinesq system with zero viscosity
In this paper we prove the global well-posedness of the two-dimensional Boussinesq system with zero viscosity for rough initial data.
On the Height of a Capillary Surface.
On the instability of solitary-wave solutions for fifth-order water wave models.
On the inversion of the camber line problem.
On the -instability and -controllability of steady flows of an ideal incompressible fluid
In the existing stability theory of steady flows of an ideal incompressible fluid, formulated by V. Arnold, the stability is understood as a stability with respect to perturbations with small in vorticity. Nothing has been known about the stability under perturbation with small energy, without any restrictions on vorticity; it was clear that existing methods do not work for this (the most physically reasonable) class of perturbations. We prove that in fact, every nontrivial steady flow is unstable...
On the local and global well-posedness theory for the KP-I equation
On the local well-posedness of a Benjamin-Ono-Boussinesq system.
On the localization of the vortices
Studiamo l'evoluzione temporale di un fluido bidimensionale incomprimibile non viscoso quando la vorticità iniziale è concentrata in regioni di diametro e mostriamo che la vorticità evoluta temporalmente è anche lei concentrata in piccole regioni di diametro , per qualunque . Noi chiamiamo questa proprietà "localizzazione". Come conseguenza abbiamo una connessione rigorosa tra il modello dei vortici puntiformi e l'Equazione di Eulero.
On the motion of a curve by its binormal curvature
We propose a weak formulation for the binormal curvature flow of curves in . This formulation is sufficiently broad to consider integral currents as initial data, and sufficiently strong for the weak-strong uniqueness property to hold, as long as self-intersections do not occur. We also prove a global existence theorem in that framework.
On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid
On the non-uniqueness of weak solution of the Euler equations
On the Numerical Resolution of the Generalized Airfoil Equation with Possio Kernel.
On the solvability of a problem of stationary fluid flow in a helical pipe.
On the three-dimensional Euler equations with a free boundary subject to surface tension
On the tidal motion around the earth complicated by the circular geometry of the ocean's shape.
On the well-balance property of Roe’s method for nonconservative hyperbolic systems. Applications to shallow-water systems
This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys. 102 (1992) 360–373]. Next, this general theory is applied to obtain well-balanced...