26 citations · 26 across the 1 of their papers we have counts for
6 papers
Unique solvability of the free-boundary Navier-Stokes equations with surface tension
Daniel Coutand, Steve Shkoller
We prove the existence and uniqueness of solutions to the time-dependent incompressible Navier-Stokes equations with a free-boundary governed by surface tension. The solution is fo…
Well-posedness and global attractors for liquid crystals on Riemannian manifolds
Steve Shkoller
We study the coupled Navier-Stokes Ginzburg-Landau model of nematic liquid crystals introduced by F.H. Lin, which is a simplified version of the Ericksen-Leslie system. We generali…
On the stability of periodic 2D Euler-alpha flows
Sergey Pekarsky, Steve Shkoller
An explicit expression is obtained for the sectional curvature in the plane spanned by two stationary flows, cos(k, x) and cos(l, x). It is shown that for certain values of the wav…
Smooth global Lagrangian flow for the 2D Euler and second-grade fluid equations
Steve Shkoller
We present a very simple proof of the global existence of a Lagrangian flow map for the 2D Euler and second-grade fluid equations (on a compact Riemannian manifold with…
On Incompressible Averaged Lagrangian Hydrodynamics
Steve Shkoller
This paper is devoted to the geometric analysis of the incompressible averaged Euler equations on compact Riemannian manifolds with boundary. The equation also coincides with the m…
Geometry and curvature of diffeomorphism groups with metric and mean hydrodynamics
Steve Shkoller
Recently, Holm, Marsden, and Ratiu [1998] have derived a new model for the mean motion of an ideal fluid in Euclidean space given by the equation $\dot{V}(t) + \nabla_{U(t)} V(t) -…