On oblique waves forcing by a porous cylindrical wall.
On permanent capillar-heavy waves of two liquids flowing one upon the other
On power series solutions for the Euler equation, and the Behr–Nečas–Wu initial datum
We consider the Euler equation for an incompressible fluid on a three dimensional torus, and the construction of its solution as a power series in time. We point out some general facts on this subject, from convergence issues for the power series to the role of symmetries of the initial datum. We then turn the attention to a paper by Behr, Nečas and Wu, ESAIM: M2AN 35 (2001) 229–238; here, the authors chose a very simple Fourier polynomial as an initial datum for the Euler equation and analyzed...
On reflection of shock front in multidimensional space
On singularities of capillary surfaces in the absence of gravity.
On some Boussinesq systems in two space dimensions: theory and numerical analysis
A three-parameter family of Boussinesq type systems in two space dimensions is considered. These systems approximate the three-dimensional Euler equations, and consist of three nonlinear dispersive wave equations that describe two-way propagation of long surface waves of small amplitude in ideal fluids over a horizontal bottom. For a subset of these systems it is proved that their Cauchy problem is locally well-posed in suitable Sobolev classes. Further, a class of these systems is discretized...
On Strongly Interacting Internal Solitary Waves.
On the capillarity problem with constant volume
On the chaotic behavior and the non-integrability of the four vortices problem
On the complete integrability of an equation having solitons but not known to have a lax pair.
On the computation of roll waves
The phenomenon of roll waves occurs in a uniform open-channel flow down an incline, when the Froude number is above two. The goal of this paper is to analyze the behavior of numerical approximations to a model roll wave equation which arises as a weakly nonlinear approximation of the shallow water equations. The main difficulty associated with the numerical approximation of this problem is its linear instability. Numerical round-off error can easily overtake the numerical solution and yields false...
On the Computation of Roll Waves
The phenomenon of roll waves occurs in a uniform open-channel flow down an incline, when the Froude number is above two. The goal of this paper is to analyze the behavior of numerical approximations to a model roll wave equation ut + uux = u,u(x,0) = u0(x), which arises as a weakly nonlinear approximation of the shallow water equations. The main difficulty associated with the numerical approximation of this problem is its linear instability. Numerical round-off error can easily overtake the...
On the conditional regularity of the Navier-Stokes and related equations
We present regularity conditions for a solution to the 3D Navier-Stokes equations, the 3D Euler equations and the 2D quasigeostrophic equations, considering the vorticity directions together with the vorticity magnitude. It is found that the regularity of the vorticity direction fields is most naturally measured in terms of norms of the Triebel-Lizorkin type.
On the controllability and stabilization of the linearized Benjamin-Ono equation
In this work we are interested in the study of controllability and stabilization of the linearized Benjamin-Ono equation with periodic boundary conditions, which is a generic model for the study of weakly nonlinear waves with nonlocal dispersion. It is well known that the Benjamin-Ono equation has infinite number of conserved quantities, thus we consider only controls acting in the equation such that the volume of the solution is conserved. We study also the stabilization with a feedback law which...
On the controllability and stabilization of the linearized Benjamin-Ono equation
In this work we are interested in the study of controllability and stabilization of the linearized Benjamin-Ono equation with periodic boundary conditions, which is a generic model for the study of weakly nonlinear waves with nonlocal dispersion. It is well known that the Benjamin-Ono equation has infinite number of conserved quantities, thus we consider only controls acting in the equation such that the volume of the solution is conserved. We study also the stabilization with a feedback law...
On the convective nature of roll waves instability.
On the derivation of homogeneous hydrostatic equations
On the derivation of homogeneous hydrostatic equations
In this paper we study the derivation of homogeneous hydrostatic equations starting from 2D Euler equations, following for instance [2,9]. We give a convergence result for convex profiles and a divergence result for a particular inflexion profile.
On the derivation of the nonlinear discrete equations numerically integrating the Euler PDEs.
On the Euler equations for nonhomogeneous fluids (I)