By using a new bilinear estimate, a pointwise estimate of the generalized Oseen kernel and an idea of fractional bootstrap, we show in this note that solutions to the Navier-Stokes equations with fractional dissipation are analytic in space variables.

— We present an existence resuit for the global attractor associated to the NavierStokes Equations in an infinité stnp in Ifê, and provide an estimate for Us fractal dimension in terms o f the Reynolds number

in this work, we introduce the unsteady incompressible Navier-Stokes equations with a new boundary condition, generalizes the Dirichlet and the Neumann conditions. Then we derive an adequate variational formulation of timedependent NavierStokes equations. We then prove the existence theorem and a uniqueness result. A Mixed finite-element discretization is used to generate the nonlinear system c...

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.

The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations with damping is proved for large data in three dimensional space. The model consists of the compressible Navier-Stokes equations with degenerate viscosity, and a nonlinear third-order differential operator, with the quantum Bohm potential, and the damping terms. The global weak solution...

This paper develops a least-squares approach to the solution of the incompressible Navier-Stokes equations in primitive variables. As with our earlier work on Stokes equations, we recast the Navier-Stokes equations as a first-order system by introducing a velocity flux variable and associated curl and trace equations. We show that the resulting system is well-posed, and that an associated least...

We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in R 2. We prove that the rate of dissipation of enstrophy vanishes. Stationary statistical solutions of the damped and driven Navier-Stokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations. These solutions obey the enst...

We prove global existence for a nonlinear Smoluchowski equation (a nonlinear FokkerPlanck equation) coupled with Navier-Stokes equations in 2d. The proof uses a deteriorating regularity estimate in the spirit of [5] (see also [1]) Key wordsNonlinear Fokker-Planck equations, Navier-Stokes equations, Smoluchowski equation, micro-macro interactions. AMS subject classification 35Q30, 82C31, 76A05.