In the present paper, we prove a sufficient condition of local regularity for suitable weak solutions to the Navier-Stokes equations having axial symmetry. Our condition is an axially symmetric analog of the so-called L3,∞-case in the general local regularity theory. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.

Aquasi-three-dimensional multigrid Navier–Stokes solver on singleandmultiple-passage domains is presented for solving unsteady  ows around oscillating turbine and compressor blades. The conventional direct store method is used for applying the phase-shifted periodic boundary condition over a single blade passage. A parallel version of the solver using the message passing interface standard is ...

We investigate the large time behavior of an axisymmetric model for the 3D Euler equations. In [22], Hou and Lei proposed a 3D model for the axisymmetric incompressible Euler and Navier-Stokes equations with swirl. This model shares many properties of the 3D incompressible Euler and Navier-Stokes equations. The main difference between the 3D model of Hou and Lei and the reformulated 3D Euler an...

We study regularity of viscous incompressible fluid flows in a 2D channel with “do nothing” outflow boundary condition on the output for the steady Stokes and Navier–Stokes equations. Mathematics Subject Classification (2000). 35Q30; 74G55; 74G20.

We consider the Cauchy problem for the incompressible Navier-Stokes equations in R3, and provide a sufficient condition to ensure the smoothness of the solution. It involves only two entries of the velocity Hessian.

Using a weak convergence approach, we prove a LPD for the solution of 2D stochastic Navier Stokes equations when the viscosity converges to 0 and the noise intensity is multiplied by the square root of the viscosity. Unlike previous results on LDP for hydrodynamical models, the weak convergence is proven by tightness properties of the distribution of the solution in appropriate functional spaces.

The dynamics of capillary pinching of a fluid thread are described by similarity solutions of the Navier–Stokes equations. Eggers @Phys. Rev. Lett. 71, 3458 ~1993!# recently proposed a single universal similarity solution for a viscous thread pinching with an inertial–viscous–capillary balance in an inviscid environment. In this paper it is shown that there is actually a countably infinite fami...

We consider complex-valued solutions of the three-dimensional NavierStokes system without external forcing on R. We show that there exists an open set in the space of 10-parameter families of initial conditions such that for each family from this set there are values of parameters for which the solution develops blow up in finite time.

An overview of recent experimental results on instability and dynamics of jets at low Reynolds numbers is given. Round and plane, macro and micro jets are under the consideration. Basic features of their evolution affected by initial conditions at the nuzzle outlet and environmental perturbations are demonstrated.