In this article, we study the steady generalized Navier-Stokes equations in a half-space in the setting of variable exponent spaces. We first establish variable exponent spaces of Clifford-valued functions in a half-space. Then, using this operator theory together with the contraction mapping principle, we obtain the existence and uniqueness of solutions to the stationary Navier-Stokes equation...

In this paper statistical solutions of the 3D Navier-Stokes-α model with periodic boundary condition are considered. It is proved that under certain natural conditions statistical solutions of the 3D Navier-Stokes-α model converge to statistical solutions of the exact 3D Navier-Stokes equations as α goes to zero. The statistical solutions considered here arise as families of time-projections of...

In this paper, we prove the existence and uniqueness of a smooth solution to a tamed 3D Navier-Stokes equation in the whole space. In particular, if there exists a bounded smooth solution to the classical 3D Navier-Stokes equation, then this solution satisfies our tamed equation. Moreover, using this renomalized equation we can give a new construction for a suitable weak solution of the classic...

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 or...

This paper studies the quasi-neutral limit of pressureless Navier-Stokes-Poisson equations in plasma physics in the torus T. For well prepared initial data the convergence of solutions of compressible Navier-Stokes-Poisson equations to the solutions of incompressible Navier-Stokes equations is justified rigorously by using the curl-div decomposition of the gradient. And a priori estimates with ...

Abstract. We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in R with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the Navier boundary condition in terms of the vorticity, which is motivated by the Hodge theory on manifolds with boundary from the viewpoint of differential...

This paper presents an improved gas-kinetic scheme based on the Bhatnagar-Gross-Krook (BGK) model for the compressible Navier-Stokes equations. The current method extends the previous gaskinetic Navier-Stokes solver developed by Xu and Prendergast by implementing a general nonequilibrium state to represent the gas distribution function at the beginning of each time step. As a result, the requir...

We study the partial regularity of a 3D model of the incompressible Navier-Stokes equations which was recently introduced by the authors in [11]. This model is derived for axisymmetric flows with swirl using a set of new variables. It preserves almost all the properties of the full 3D Euler or Navier-Stokes equations except for the convection term which is neglected in the model. If we add the ...

We consider solutions to the Navier-Stokes equations with Navier boundary conditions in a bounded domain Ω in R with a Cboundary Γ. Navier boundary conditions can be expressed in the form ω(v) = (2κ−α)v · τ and v ·n = 0 on Γ, where v is the velocity, ω(v) the vorticity, n a unit normal vector, τ a unit tangent vector, and α is in L∞(Γ). Such solutions have been considered in [2] and [3], and, i...

In this paper we prove the logarithmically improved Beale-Kato-Majda's criterion to the three-dimensional incompressible Euler and Navier-Stokes equations as well as the logarithmically improved Serrin's criteria to the three-dimensional incompressible Navier-Stokes equations.