Asymptotic behavior for the Navier – Stokes equations with nonzero external
نویسندگان
چکیده
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 shows that the Stokes solution does not decay ∧ quickly. © 2008 Published by Elsevier Ltd
منابع مشابه
Regularity and asymptotic behaviour of the solutions of the Navier-Stokes equations with diffusion
In this paper we consider the motion of a continuous medium consisting of two components, for example pure and salt water, with a diffusion effect obeying Fick’s law. We prove, for small data and external force, the regularity of the solution in the Hilbert space Hk, with k ≥ 2, and the exponential asymptotic convergence to the solutions of the homogeneous Navier-Stokes equations.
متن کاملLp-SOLUTIONS OF THE STEADY-STATE NAVIER–STOKES WITH ROUGH EXTERNAL FORCES
In this paper we address the existence, the asymptotic behavior and stability in L and L, 3 2 < p ≤ ∞, for solutions to the steady state 3D Navier-Stokes equations with possibly very singular external forces. We show that under certain smallness conditions of the forcing term there exists solutions to the stationary Navier-Stokes equations in L spaces, and we prove the stability of these soluti...
متن کاملL-Solutions of the Steady-State Navier–Stokes Equations with Rough External Forces
In this paper we address the existence, the asymptotic behavior and stability in L and L , 3 2 < p ≤ , for solutions to the steady state 3D Navier–Stokes equations with possibly very singular external forces. We show that under certain smallness conditions of the forcing term there exists solutions to the stationary Navier–Stokes equations in L spaces, and we prove the stability of these soluti...
متن کاملAsymptotic stability for the Navier-Stokes equations in the marginal class
In this paper we consider the Navier-Stokes equations in R, n ≥ 3. We prove the asymptotic stability for weak solutions in the marginal class u ∈ L2(0,∞; BMO) with arbitrary initial and external perturbations. Mathematics Subject Classification(2000): 35Q30, 93D20
متن کاملOptimization with the time-dependent Navier-Stokes equations as constraints
In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...
متن کامل