Uniform exponential stability of the Ekman spiral

Uniform Exponential Stability ofApproximations in Linear Viscoelasticity

In this paper, we rst study the abstract setting of linear vis-coelasticity and under reasonable conditions on the kernel we prove the exponential stability of the associated semigroup. Secondly, we study the general approximate schemes proposed by Banks and Burns, by Ito and Kappel, and by Fabiano and Ito, respectively. The uniformly exponential stability of semigroups associated with these ap...

On the uniform exponential stability of linear time-delay systems

This paper deals with the global uniform exponential stability independent of delay of timedelay linear and time-invariant systems subject to point and distributed delays for the initial conditions being continuous real functions except possibly on a set of zero measure of bounded discontinuities. It is assumed that the delay-free system as well as an auxiliary one are globally uniformly expone...

Stability of Mixed Ekman - Hartmann

Uniform exponential stability for evolution families on the half-line

In this paper we give a characterization for the uniform exponential stability of evolution families {Φ(t, t0)}t≥t0 on R+ that do not have an exponential growth, using the hypothesis that the pairs of function spaces (L1(X), L∞(X)) and (Lp(X), Lq(X)), (p, q) 6= (1,∞), are admissible to the evolution families.

Nonlinear stability of Ekman boundary layers

Consider the initial value problem for the three dimensional Navier-Stokes equations with rotation in the half-space R+ subject to Dirichlet boundary conditions as well as the Ekman spiral which is a stationary solution to the above equations. It is proved that the Ekman spiral is nonlinearly stable with respect to L2-perturbations provided the corresponding Reynolds number is small enough. Mor...