We estimate the asymptotic behavior for the Stokes solutions, with external forces first. We ∧ found that if there ∧ are external forces, then the energy decays ∧ slowly even if the forces ∧ decay quickly. Then, we also obtain the asymptotic ∧ behavior in the temporal-spatial direction for weak solutions of the Navier–Stokes equations. We also provide a simple example of external forces which s...

Recent adaptive feedback control experiments demonstrated control of transient i.e. nonimpulsive Stokes emission from two closely spaced Raman-active modes in liquid methanol e.g., B. J. Pearson et al., Phys. Rev. A 63, 063412 2001 . Optimally shaped pulses were found that selectively excited one of the two Stokes lines alone, optimized emission from both modes together, or completely suppresse...

In the ambit of the mini course, to which I have been kindly invited to participate, I would like to develop some results concerning the Stokes and Navier-Stokes initial boundary value problems with nondecaying data. To better explain the aims, we split the case of the Stokes problem from the one of the Navier-Stokes. The Stokes initial boundary value problem with nondecaying data is essentiall...

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 ...

There has been a surge of work on models for coupling surface-water with groundwater flows which is at its core the Stokes-Darcy problem. The resulting (Stokes-Darcy) fluid velocity is important because the flow transports contaminants. The analysis of models including the transport of contaminants has, however, focused on a quasi-static Stokes-Darcy model. Herein we consider the fully evolutio...

The quantum theory of forward Stokes generation by means of stimulated Raman scattering is extended to the case of a colored (finite-bandwidth) chaotic pump, which has both amplitude and phase fluctuations. In both transient and steady-state limits the mean Stokes intensity is found to be enhanced over that resulting from a coherent pump. In the limit that the chaotic-pump bandwidth becomes lar...

We study in this article both the structure and the structural evolution of the solutions of 2-D Navier-Stokes equations with periodic boundary conditions and the evolution of their solutions. First the structure of all eigenvectors of the corresponding Stokes problem is classified using a block structure, and is linked to the typical structure of the Taylor vortices. Then the structure of the ...

In recent years there has been lots of interest in the use of first-order system leastsquares method (FOSLS) for numerical approximations of elliptic partial differential equations, Stokes equations, elasticity and Navier-Stokes equations. In this paper we will provide a brief review of FOSLS around elliptic problems and Stokes equations. FOSLS is to find a minimization solution which minimizes...

Problem statement: We consider the numerical solvers for the linearized Navier-Stokes problem. Both the Stokes problem and Oseen problems are considered. Approach: We used the Mark and Cell (MAC) discretization method to discretize the Navier-Stokes equations. We used preconditioned Krylov subspace methods to solve the resulting linear systems. Results: Numerical experimental results are perfor...