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Long-time behavior of the Stokes-transport system in a channel
We consider here a two-dimensional incompressible fluid in a periodic channel, whose density is advected by pure transport, and whose …
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Long-time behavior of the Stokes-transport system in a channel
Hyperbolicity of a semi-Lagrangian formulation of the hydrostatic free-surface Euler system
By a semi-Lagrangian change of coordinates, the hydrostatic Euler equations describing free-surface sheared flows is rewritten as a …
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Hyperbolicity of a semi-Lagrangian formulation of the hydrostatic free-surface Euler system
Numerical investigations of non-uniqueness for the Navier–Stokes initial value problem in borderline spaces
We consider the Cauchy problem for the incompressible Navier–Stokes equations in $\mathbb{R}^3$ for a one-parameter family of explicit …
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Numerical investigations of non-uniqueness for the Navier–Stokes initial value problem in borderline spaces
Existence and uniqueness for plane stationary Navier–Stokes flows with compactly supported force
We study the stationary Navier–Stokes equations in the whole plane with a compactly supported force term and with a prescribed constant …
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Existence and uniqueness for plane stationary Navier–Stokes flows with compactly supported force
Nonlinear stability at the Eckhaus boundary
The real Ginzburg–Landau equation possesses a family of spatially periodic equilibria. If the wave number of an equilibrium is strictly …
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Nonlinear stability at the Eckhaus boundary
Existence and uniqueness of steady weak solutions to the Navier–Stokes equations in $\mathbb{R}^2$
The existence of weak solutions to the stationary Navier–Stokes equations in the whole plane $\mathbb{R}^2$ is proven. This particular …
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Existence and uniqueness of steady weak solutions to the Navier–Stokes equations in $\mathbb{R}^2$
Optimal asymptotic behavior of the vorticity of a viscous flow past a two-dimensional body
The asymptotic behavior of the vorticity for the steady incompressible Navier–Stokes equations in a two-dimensional exterior domain is …
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Optimal asymptotic behavior of the vorticity of a viscous flow past a two-dimensional body
On the asymptotic stability of steady flows with nonzero flux in two-dimensional exterior domains
The Navier–Stokes equations in a two-dimensional exterior domain are considered. The asymptotic stability of stationary solutions …
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On the asymptotic stability of steady flows with nonzero flux in two-dimensional exterior domains
On the stationary Navier–Stokes equations in the half-plane
We consider the stationary incompressible Navier–Stokes equation in the half-plane with inhomogeneous boundary condition. We prove the …
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On the stationary Navier–Stokes equations in the half-plane
Generalized scale-invariant solutions to the two-dimensional stationary Navier–Stokes equations
New explicit solutions to the incompressible Navier–Stokes equations in $\mathbb{R}^2 \setminus \{0\}$ are determined, which generalize …
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Generalized scale-invariant solutions to the two-dimensional stationary Navier–Stokes equations