52 citations · 133 across the 13 of their papers we have counts for
13 papers
Forward self-similar solutions to the 2D Navier--Stokes equations
Dallas Albritton, Julien Guillod, Mikhail Korobkov +1
We construct self-similar solutions to the 2D Navier--Stokes equations evolving from arbitrarily large --homogeneous initial data and present numerical evidence for their non-u…
Hyperbolicity of a semi-Lagrangian formulation of the hydrostatic free-surface Euler system
Bernard Di Martino, Chourouk El Hassanieh, Edwige Godlewski +2
By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a system of quasilinear equations, where stability…
Long-time behavior of the Stokes-transport system in a channel
Anne-Laure Dalibard, Julien Guillod, Antoine Leblond
We consider here a two-dimensional incompressible fluid in a periodic channel, whose density is advected by pure transport, and whose velocity is given by the Stokes equation with…
Existence and uniqueness for plane stationary Navier-Stokes flows with compactly supported force
Julien Guillod, Mikhail Korobkov, Xiao Ren
We study the stationary Navier--Stokes equations in the whole plane with a compactly supported force term and with a prescribed constant spatial limit. Prior to this work, existenc…
Nonlinear stability at the Eckhaus boundary
Julien Guillod, Guido Schneider, Peter Wittwer +1
The real Ginzburg-Landau equation possesses a family of spatially periodic equilibria. If the wave number of an equilibrium is strictly below the so called Eckhaus boundary the equ…
Numerical investigations of non-uniqueness for the Navier-Stokes initial value problem in borderline spaces
Julien Guillod, Vladimír Šverák
We consider the Cauchy problem for the incompressible Navier-Stokes equations in for a one-parameter family of explicit scale-invariant axi-symmetric initial data, w…
Existence and uniqueness of steady weak solutions to the Navier-Stokes equations in
Julien Guillod, Peter Wittwer
The existence of weak solutions to the stationary Navier-Stokes equations in the whole plane is proven. This particular geometry was the only case left open since th…
On the asymptotic stability of steady flows with nonzero flux in two-dimensional exterior domains
Julien Guillod
The Navier-Stokes equations in a two-dimensional exterior domain are considered. The asymptotic stability of stationary solutions satisfying a general hypothesis is proven under an…
Steady solutions of the Navier-Stokes equations in the plane
Julien Guillod
This study is devoted to the incompressible and stationary Navier-Stokes equations in two-dimensional unbounded domains. First, the main results on the construction of the weak sol…
Optimal asymptotic behavior of the vorticity of a viscous flow past a two-dimensional body
Julien Guillod, Peter Wittwer
The asymptotic behavior of the vorticity for the steady incompressible Navier-Stokes equations in a two-dimensional exterior domain is described in the case where the velocity at i…
On the stationary Navier-Stokes equations in the half-plane
Julien Guillod, Peter Wittwer
We consider the stationary incompressible Navier-Stokes equation in the half-plane with inhomogeneous boundary condition. We prove existence of strong solutions for boundary data c…
Generalized scale-invariant solutions to the two-dimensional stationary Navier-Stokes equations
Julien Guillod, Peter Wittwer
New explicit solutions to the incompressible Navier-Stokes equations in are determined, which generalize the scale-invariant…
Asymptotic behaviour of solutions to the stationary Navier-Stokes equations in two dimensional exterior domains with zero velocity at infinity
Julien Guillod, Peter Wittwer
We investigate analytically and numerically the existence of stationary solutions converging to zero at infinity for the incompressible Navier-Stokes equations in a two-dimensional…