93,538 research outputs found
Algorithm development
The past decade has seen considerable activity in algorithm development for the Navier-Stokes equations. This has resulted in a wide variety of useful new techniques. Some examples for the numerical solution of the Navier-Stokes equations are presented, divided into two parts. One is devoted to the incompressible Navier-Stokes equations, and the other to the compressible form
Global regularity for a family of 3D models of the axisymmetric Navier-Stokes equations
We consider a family of 3D models for the axi-symmetric incompressible
Navier-Stokes equations. The models are derived by changing the strength of the
convection terms in the axisymmetric Navier-Stokes equations written using a
set of transformed variables. We prove the global regularity of the family of
models in the case that the strength of convection is slightly stronger than
that of the original Navier-Stokes equations, which demonstrates the potential
stabilizing effect of convection
A Liouville theorem for the planer Navier-Stokes equations with the no-slip boundary condition and its application to a geometric regularity criterion
We establish a Liouville type result for a backward global solution to the
Navier-Stokes equations in the half plane with the no-slip boundary condition.
No assumptions on spatial decay for the vorticity nor the velocity field are
imposed. We study the vorticity equations instead of the original Navier-Stokes
equations. As an application, we extend the geometric regularity criterion for
the Navier-Stokes equations in the three-dimensional half space under the
no-slip boundary condition
Inviscid limit of stochastic damped 2D Navier-Stokes equations
We consider the inviscid limit of the stochastic damped 2D Navier- Stokes
equations. We prove that, when the viscosity vanishes, the stationary solution
of the stochastic damped Navier-Stokes equations converges to a stationary
solution of the stochastic damped Euler equation and that the rate of
dissipation of enstrophy converges to zero. In particular, this limit obeys an
enstrophy balance. The rates are computed with respect to a limit measure of
the unique invariant measure of the stochastic damped Navier-Stokes equations
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