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math.AP2026
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…
math.AP2023
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…
math.AP2018
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…