Linear stability and instability of relativistic Vlasov‐Maxwell systems

We consider the linear stability problem for a symmetric equilibrium of the relativistic Vlasov‐Maxwell (RVM) system. For an equilibrium whose distribution function depends monotonically on the particle energy, we obtain a sharp linear stability criterion. The growing mode is proved to be purely growing, and we get a sharp estimate of the maximal growth rate. In this paper we specifically treat the periodic 1½D case and the 3D whole‐space case with cylindrical symmetry. We explicitly illustrate, using the linear stability criterion in the 1½D case, several stable and unstable examples. © 2006 Wiley Periodicals, Inc.     

Exact steady periodic water waves with vorticity

We consider the classical water wave problem described by the Euler equations with a free surface under the influence of gravity over a flat bottom. We construct two‐dimensional inviscid periodic traveling waves with vorticity. They are symmetric waves whose profiles are monotone between each crest and trough. We use bifurcation and degree theory to construct a global connected set of such solutions. © 2003 Wiley Periodicals, Inc.