189 citations · 250 across the 13 of their papers we have counts for
15 papers
Global existence and convergence near equilibrium for the moving interface problem between Navier-Stokes and the linear wave equation
Daniel Coutand
We first establish existence for all positive time near equilibrium for the moving interface problem between the Navier-Stokes equations for the evolving fluid phase (moved by the…
Finite time singularity formation for moving interface Euler equations
Daniel Coutand
This paper proposes a new general methodology for finite-time singularity formation for moving interface problems involving the incompressible Euler equations in the plane. The fir…
Regularity of the velocity field for Euler vortex patch evolution
Daniel Coutand, Steve Shkoller
We consider the vortex patch problem for both the 2-D and 3-D incompressible Euler equations. In 2-D, we prove that for vortex patches with Sobolev-class contour regula…
On the splash singularity for the free-surface of a Navier-Stokes fluid
Daniel Coutand, Steve Shkoller
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface self-intersects in finite time. We prove that for -dimensional flows, or , the…
On the impossibility of finite-time splash singularities for vortex sheets
Daniel Coutand, Steve Shkoller
In fluid dynamics, an interface splash singularity occurs when a locally smooth interface self-intersects in finite time. By means of elementary arguments, we prove that such a sin…
Global existence and decay for solutions of the Hele-Shaw flow with injection
C. H. Arthur Cheng, Daniel Coutand, Steve Shkoller
We study the global existence and decay to spherical equilibrium of Hele-Shaw flows with surface tension. We prove that without injection of fluid, perturbations of the sphere deca…