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We study the problem of conformal deformation of Riemannian structure to constant scalar curvature with zero mean curvature on the boundary. We prove compactness for the full set of solutions when… (More)

Bray and Khuri (2011 Asian J. Math. 15 557–610; 2010 Discrete Continuous Dyn. Syst. A 27 741766) outlined an approach to prove the Penrose inequality for general initial data sets of the Einstein… (More)

Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235(Dated: September 18, 2014)We examine the cosmological consequences of an alternative to the standard expression for… (More)

Abstract We study the free boundary Euler equations with surface tension in three spatial dimensions, showing that the equations are well-posed if the coefficient of surface tension is positive. Then… (More)

Using a simple and well-motivated modification of the stress-energy tensor for a viscous fluid proposed by Lichnerowicz, we prove that Einstein's equations coupled to a relativistic version of the… (More)

We study the problem of coupling Einstein’s equations to a physically well-motivated relativistic modification of the Navier-Stokes equations. Under a technical condition for the vorticity, we prove… (More)

In this letter, we prove that non-trivial compact Yamabe solitons or breathers do not exist. In particular our proof in the two dimensional case depends only on properties of the determimant of the… (More)

Abstract We consider the generalization of the Navier–Stokes equation from R n to the Riemannian manifolds. There are inequivalent formulations of the Navier–Stokes equation on manifolds due to the… (More)

We study the free boundary Euler equations in two spatial dimensions. We prove that if the boundary has constant curvature, then solutions of the free boundary fluid motion converge to solutions of… (More)

We derive a priori estimates for the incompressible free-boundary Euler equations with surface tension in three spatial dimensions. Working in Lagrangian coordinates, we provide a priori estimates… (More)