1 citations · 1 across the 4 of their papers we have counts for
4 papers · 1 filter
On some properties of the curl operator and their consequences for the Navier-Stokes system
Nicolas Lerner, François Vigneron
We investigate some geometric properties of the operator, based on its diagonalizationand its expression as a non-local symmetry of the pseudo-derivative $(-Δ…
Regularity of solutions of a fractional porous medium equation
Cyril Imbert, Rana Tarhini, François Vigneron
This article is concerned with a porous medium equation whose pressure law is both nonlinear and nonlocal, namely $\partial_t u = { \nabla \cdot} \left(u \nabla(-Δ)^{\fracα{2}-1}u^…
Free Turbulence on R^3 and T^3
François Vigneron
The hydrodynamics of Newtonian fluids has been the subject of a tremendous amount of work over the past eighty years, both in physics and mathematics. Sadly, however, a mutual feel…
On the localization of the magnetic and the velocity fields in the equations of magnetohydrodynamics
Lorenzo Brandolese, François Vigneron
We study the behavior at infinity, with respect to the space variable, of solutions to the magnetohydrodynamics equations in . We prove that if the initial magnetic fiel…