相关论文: From Petrov-Einstein to Navier-Stokes in Spatially…
We consider a p+1-dimensional timelike hypersurface \Sigma_c embedded with a flat induced metric in a p+2-dimensional Einstein geometry. It is shown that imposing a Petrov type I condition on the geometry reduces the degrees of freedom in…
Recently it has been shown that imposing Petrov type I condition on the boundary may reduce the Einstein's equation to the Navier-Stokes equation in the non-relativistic and near-horizon limit. In this paper we extend this framework to a…
Previously it has been shown that imposing a Petrov-like boundary condition on a hypersurface may reduce the Einstein equation to the incompressible Navier-Stokes equation, but all these correspondences are established in the near horizon…
Recently Lysov and Strominger [arXiv:1104.5502] showed that imposing Petrov type I condition on a $(p+1)$-dimensional timelike hypersurface embedded in a $(p+2)$-dimensional vacuum Einstein gravity reduces the degrees of freedom in the…
Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…
The incompressible Navier-Stokes equations are re-formulated to involve an arbitrary time dilation; and in this manner, the modified Navier-Stokes equations are obtained which have some penalization terms in the right hand side. Then, the…
In this paper we generalize the previous works to the case that the near-horizon dynamics of the Einstein-Dilaton-Axion theory can be governed by the incompressible Navier-Stokes equation via imposing the Petrov-like boundary condition on…
We show by explicit construction that for every solution of the incompressible Navier-Stokes equation in $p+1$ dimensions, there is a uniquely associated "dual" solution of the vacuum Einstein equations in $p+2$ dimensions. The dual…
The Petrov type I condition for the solutions of vacuum Einstein equations in both of the non-relativistic and relativistic hydrodynamic expansions is checked. We show that it holds up to the third order of the non-relativistic hydrodynamic…
We deal with the incompressible Navier-Stokes equations, in two and three dimensions, when some vortex patches are prescribed as initial data i.e. when there is an internal boundary across which the vorticity is discontinuous. We show…
We study the compressible Navier-Stokes system driven by physically relevant transport noise, where the noise influences both the continuity and momentum equations. Our approach is based on transforming the system into a partial…
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in $\R^n$ with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat…
Hydrodynamics of the non-relativistic compressible fluid in the curved spacetime is derived using the generalized framework of the stochastic variational method (SVM) for continuum medium. The fluid-stress tensor of the resultant equation…
We consider the Navier-Stokes system describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier's slip boundary conditions. It is shown that…
We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a…
Recently the Petrov type I condition is introduced to reduce the degrees of freedom in the extrinsic curvature of a timelike hypersurface to the degrees of freedom in the dual Rindler fluid in Einstein gravity. In this paper we show that…
The Navier-Stokes equation describes the deterministic evolution of incompressible fluids. The effects of random initial conditions on solutions of this equation are studied. It is shown that there is an infrared stable fixed point…
We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed…
We show that in bounded domains with no-slip boundary conditions, the Navier-Stokes pressure can be determined in a such way that it is strictly dominated by viscosity. As a consequence, in a general domain we can treat the Navier-Stokes…
The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an…