A weak instability mode, associated with phase-locked counterpropagating coastal Kelvin waves in horizontal anticyclonic shear, is found in the semigeostrophic (SG) equations for stratified flow in a channel. This SG instability mode approximates a similar mode found in the Euler equations in the limit in which particle-trajectory slopes are much smaller than f /N, where f is the Coriolis frequ...

We introduce mountain-pass type arguments in the context of orbital instability for Klein-Gordon equations. Our aim is to illustrate on two examples how these arguments can be useful to simplify proofs and derive new results of orbital stability/instability. For a power-type nonlinearity, we prove that the ground states of the associated stationary equation are minimizers of the functional acti...

Using WKB methods for very small times, we prove some instability phenomena for semi-classical (linear or) nonlinear Schrödinger equations. Like in several recent papers concerned with instability or ill-posedness issues, the main step of the analysis consists in reducing the problem to an ordinary differential equation. The solution to this o.d.e. is explicit, and the instability mechanism is ...

Using WKB methods for very small times, we prove some instability phenomena for semi-classical (linear or) nonlinear Schrödinger equations. Like in several recent papers concerned with instability or ill-posedness issues, the main step of the analysis consists in reducing the problem to an ordinary differential equation. The solution to this o.d.e. is explicit, and the instability mechanism is ...

A theoretical study analyzing three-dimensional combustion acoustic instabilities in a liquid propellant rocket engine combustor has been conducted. A linear theory based on Crocco’s pressure sensitive time lag model is used. To apply this theory the combustor is divided into two main components, including the combustion chamber and the converging part of the nozzle. The assumption of concentra...

We formulate the relativistic implicit time-dependent Vlasov-Maxwell’s system based on the simplified implicit Maxwell solver. An implicit finite difference algorithm is developed to solve the Maxwell’s equations and equations of motion without coupling to each other, and is implemented to a newly developed 1d3v code. We test the code against the two stream instability, ion acoustic wave dampin...

It is proved, using a bootstrap argument, that linear instability implies nonlinear instability for the incompressible Navier-Stokes equations in L for all p ∈ (1,∞) and any finite or infinite domain in any dimension n.

We consider a two-group asset flow model of a financial instrument with one group focused on price trend, the other on value. We prove the existence of both stable and unstable regions for the system of differential equations and show that a strong motivation based on (particularly recent) price trend is associated with instability. Numerical computations using a set of typical parameters descr...

We show that the perturbation theory for dual semigroups (sun-star-calculus) that has proved useful for analyzing delay-differential equations is equally efficient for dealing with Volterra functional equations. In particular, we obtain both the stability and instability parts of the principle of linearized stability and the Hopf bifurcation theorem. Our results apply to situations in which the...

The simultaneous forward and backward stimulated Brillouin scattering (SBS) of crossed laser beams is studied in detail. Analytical solutions are obtained for the linearized equations governing the transient phase of the instability and the nonlinear equations governing the steady state. These solutions show that backward SBS dominates the initial evolution of the instability, whereas forward S...