180 citations · 321 across the 4 of their papers we have counts for
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Solvability and regularity for an elliptic system prescribing the curl, divergence, and partial trace of a vector field on Sobolev-class domains
C. H. Arthur Cheng, Steve Shkoller
We provide a self-contained proof of the solvability and regularity of a Hodge-type elliptic system, wherein the divergence and curl of a vector field are prescribed in an open, bo…
A priori estimates for the free-boundary 3-D compressible Euler equations in physical vacuum
Daniel Coutand, Hans Lindblad, Steve Shkoller
We prove a priori estimates for the three-dimensional compressible Euler equations with moving {\it physical} vacuum boundary, with an equation of state given by fo…
On the interaction between quasilinear elastodynamics and the Navier-Stokes equations
Daniel Coutand, Steve Shkoller
The interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations, coupled to one another along the moving material interfac…
The anisotropic averaged Euler equations
Jerrold E. Marsden, Steve Shkoller
The purpose of this paper is to derive the anisotropic averaged Euler equations and to study their geometric and analytic properties. These new equations involve the evolution of a…