This article is devoted to the study of the nonhomogeneous incompressible Navier-Stokes equations in space dimension three. By making use of the “weakly nonlinear” energy estimate approach introduced by Lei and Zhou in [16], we establish two logarithmically improved blow-up criteria of the strong or smooth solutions subject to vacuum for the 3D nonhomogeneous incompressible Navier-Stokes equati...

Compared to conventional techniques in computational fluid dynamics, the lattice Boltzmann method (LBM) seems to be a completely different approach to solve the incompressible Navier-Stokes equations. The aim of this article is to correct this impression by showing the close relation of LBM to two standard methods: relaxation schemes and explicit finite difference discretizations. As a side eff...

We give another proof of a theorem of Scharlemann and Tomova and of a theorem of Hartshorn. The two theorems together say the following. Let M be a compact orientable irreducible 3–manifold and P a Heegaard surface of M . Suppose Q is either an incompressible surface or a strongly irreducible Heegaard surface in M . Then either P ∩ Q = ∅ after an isotopy or the Hempel distance d(P ) ≤ 2genus(Q)...

In this paper we describe and analyze a two-level method for discretizing the equations of stationary, viscous, incompressible magnetohydrodynamics. The MHD equations model the ow of a viscous, incompressible, electrically conducting uid, interacting with magnetic and electric elds. These arise in plasma physics, nuclear reactor technology, and geophysics. The suggested algorithm involves solvi...

Let M be a closed, irreducible, genus two 3–manifold, and F a maximal collection of pairwise disjoint, closed, orientable, incompressible surfaces embedded in M . Then each component manifold Mi of M − F has handle number one, i.e. admits a Heegaard splitting obtained by attaching a single 1–handle to one or two components of ∂Mi. This result also holds for a decomposition of M along a maximal ...

In this paper we consider the numerical simulations of the incompressible materials on an unbounded domain in <2. A series of artificial boundary conditions at a circular artificial boundary for solving incompressible materials on an unbounded domain is given. Then the original problem is reduced to a problem on a bounded domain, which be solved numerically by a mixed finite element method. The...

I study the possible phase transitions when two layers at filling factor νt = 1 are gradually separated. In the bosonic case the system should undergo a pairing transition from a Fermi liquid to an incompressible state. In the Fermionic case, the state evolves from an incompressible (1, 1, 1) state to a Fermi liquid. I speculate that there is an intermediate phase involving charge two quasipart...

Zang, T.A., On the rotation and skew-symmetric forms for incompressible flow simulations, Applied Numerical Mathematics 7 (1991) 27-40. A variety of numerical simulations of transition and turbulence in incompressible flow are presented to compare the commonly used rotation form with the skew-symmetric (and other) forms of the nonlinear terms. The results indicate that the rotation form is much...