We present here the homogenization of the equations for the initial modulational (large scale) perturbations of stationary solutions of the two-dimensional Navier–Stokes equations with a time-independent periodic rapidly oscillating forcing. The stationary solutions are cellular flows and they are determined by the stream function φ = sinx1/ sinx2/ + δ cosx1/ cosx2/ , 0 ≤ δ ≤ 1. Two results are...

We consider a general model of chemotaxis with finite speed of propagation in one space dimension. For this model we establish a general result of global stability of some constant states both for the Cauchy problem on the whole real line and for the Neumann problem on a bounded interval. These results are obtained using the linearized operators and the accurate analysis of their nonlinear pert...

Periodic waves of the one-dimensional cubic defocusing NLS equation are considered. Using tools from integrability theory, these waves have been shown in [4] to be linearly stable and the Floquet–Bloch spectrum of the linearized operator has been explicitly computed. We combine here the first four conserved quantities of the NLS equation to give a direct proof that cnoidal periodic waves are or...

We address the question of bounds on the synchronization error for the case of nearly identical nonlinear systems. It is pointed out that negative largest conditional Lyapunov exponents of the synchronization manifold are not sufficient to guarantee a small synchronization error and that one has to find bounds for the deformation of the manifold due to perturbations. We present an analytic boun...

The existence of a time periodic solution of the compressible Navier-Stokes equation on the whole space is proved for sufficiently small time periodic external force when the space dimension is greater than or equal to 3. The proof is based on the spectral properties of the time-T -map associated with the linearized problem around the motionless state with constant density in some weighted L∞ a...

An analytical discrete-ordinates method is used to solve the temperature-jump problem as defined by a synthetic-kernel model of the linearized Boltzmann equation. In particular, the temperature and density perturbations and the temperature-jump coefficient defined by the CES model equation are obtained (essentially) analytically in terms of a modern version of the discrete-ordinates method. The...

Polynomial expansion procedures, along with an analytical discrete-ordinates method, are used to solve the temperature-jump problem based on a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions. In particular, the temperature and density perturbations and the temperature-jump coe5cient are obtained (essentially) analytically in terms of a modern version of the d...

The hydrodynamic instability of one-dimensional flow of electrons in an ungated semiconductor driven by a voltage difference is studied. The governing transport and electrostatic equations are linearized about the steady flow, and the eigenspectrum of perturbations is calculated. The carrier flow is found to be unstable under certain circumstances through oscillations that manifest themselves a...

In this work the local equations governing the dynamics of fluidized beds are written in terms of averaged variables and constitutive relations based on physical arguments are proposed. The averaged equations are perturbed with small disturbances from the homogeneous fluidization state, and linearized with respect to the perturbations. A stability analysis is carried out and shows that the part...

A new stability investigation method based on normal modes of linearized free-surface perturbations is presented. Stability criteria, for each temporal schemes, are deduced from this method via a symbolic computation of the two eigenvalues of the amplification matrix, allowing us to choose the optimal time step in a straightforward manner. Moreover, efficient semi-implicit schemes well adapted ...