LX. On stationary waves in flowing water.—Part III

Lx-STABILITY OF STATIONARY DISCRETE SHOCKS

The nonlinear stability in the //-norm, p > 1 , of stationary weak discrete shocks for the Lax-Friedrichs scheme approximating general m x m systems of nonlinear hyperbolic conservation laws is proved, provided that the summations of the initial perturbations equal zero. The result is proved by using both a weighted estimate and characteristic energy method based on the internal structures of t...

Roll waves on flowing cornstarch suspensions

We report a traveling wave instability in low Reynolds number flows of aqueous concentrated suspensions of corn starch. The experimental observations are difficult to reconcile with theoretical predictions based on simple rheological models which indicate that flows are stable at low Reynolds number.  2005 Elsevier B.V. All rights reserved.

Onset of spatially chaotic waves on flowing films.

Action-angle representation of waves and instabilities in flowing plasmas

Action-angle representation of linear fluctuation in plasma is formally performed by taking the Lagrange-Hamilton theory as the basis and invoking the recent spectral technique [Hirota and Fukumoto, J. Math. Phys. 49 083101 (2008)], which is shown to be applicable equally to the magnetohydrodynamic (MHD) system and the Vlasov-Maxwell system. This formalism leads to a natural definition of the w...

Local Decay of Waves on Asymptotically Flat Stationary Space-times

In this article we study the pointwise decay properties of solutions to the wave equation on a class of stationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form of local energy decay hold forward in time we establish a t−3 local uniform decay rate for linear waves. This work was motivated by open problems concerning de...