Keywords: Rotating Navier–Stokes equations Exterior domain Boundary integral method Finite element approximation a b s t r a c t In this paper, we apply the boundary integral method to the linearized rotating Navier– Stokes equations in exterior domain. Introducing some open ball which decomposes the exterior domain into a finite domain and an infinite domain, we obtain a coupled problem by the...

We give a condition for the periodic, three dimensional, incompressible Navier-Stokes equations to be globally wellposed. This condition is not a smallness condition on the initial data, as the data is allowed to be arbitrarily large in the scale invariant space B ∞,∞, which contains all the known spaces in which there is a global solution for small data. The smallness condition is rather a non...

The no-slip boundary condition, i.e., zero fluid velocity relative to the solid at the fluid-solid interface, has been very successful in describing many macroscopic flows. A problem of principle arises when the no-slip boundary condition is used to model the hydrodynamics of immiscible-fluid displacement in the vicinity of the moving contact line, where the interface separating two immiscible ...

In this paper, we propose an adaptive finite element method for simulating the moving contact line problems in three dimensions. The model that we used is the coupled Cahn-Hilliard Navier-Stokes equations with the generalized Navier boundary condition(GNBC) proposed in [1]. In our algorithm, to improve the efficiency of the simulation, we use the residual type adaptive finite element algorithm....

We make an analytical study of the nonsteady flow of Newtonian fluids in microchannels. We consider the slip boundary condition at the solid walls with Navier hypothesis and calculate the dynamic permeability, which gives the system's response to dynamic pressure gradients. We find a scaling relation in the absence of slip that is broken in its presence. We discuss how this might be useful to e...

A coupled Legendre-Laguerre spectral element method is proposed for the Stokes and Navier-Stokes equations in unbounded domains. The method combines advantages of the high accuracy of the Laguerre-spectral method for unbounded domains and the geometric flexibility of the spectral-element method. Rigorous stability and error analysis for the Stokes problem is carried out. Numerical results indic...

Building on Evans function techniques developed to study the stability of viscous shocks, we examine the stability of viscous strong detonation wave solutions of the reacting Navier-Stokes equations. The primary result, following [1, 17], is the calculation of a stability index whose sign determines a necessary condition for spectral stability. We show that for an ideal gas this index can be ev...

We prove the global existence of weak solutions for the 2-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient (λ = λ(ρ)). Initial data and solutions are small in energy-norm with nonnegative densities having arbitrarily large sup-norm. Then, we show that if there is a vacuum domain at the initial time, then the vacuum domain will retain for all time, and vanish...

Abstract. Using method of matched asymptotic expansions, we derive the sharp interface limit for the diffusive interface model with the generalized Navier boundary condition recently proposed by Qian, Wang and Sheng in [9, 11] for the moving contact line problem. We show that the leading order problem satisfies a boundary value problem for a coupled Hale-Shaw and Navier-Stokes equations with th...

Hydrodynamic simulations of sloshing phenomena often involve the application of slip boundary condition at the wetted surfaces. If these surfaces are curved, the ambiguous nature of the normal vector in the discretized problem can interfere with the application of such a boundary condition. Even the use of consistent normal vectors, preferred from the point of view of conservation, does not ass...