Nonlinear Stability and Instability of Fluid and Plasma Equilibria

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The investigator studies the stability and instability ofequilibria in fluids and plasmas, focusing on the two-dimensionalEuler equation in fluids and on Vlasov systems in plasma physicsand stellar dynamics. He aims to develop general methods offinding linearly growing modes (especially for asymmetric modesand boundary modes), to investigate nonlinear stability undersharp linear stability criteria and for non-monotonic equilibriathat cannot be handled by the usual energy-Casimir method, and toestablish nonlinear instability from linear instability when theparticle trajectory is non-integrable. A plasma is a gas composed of particles, each carrying apositive or negative electrical charge, with approximately equalconcentrations of each charge. Most of the universe is plasma;examples include the solar wind, the ionosphere, galactic nebulae,and comet tails. Plasmas also arise in physics and engineering,for instance in nuclear fusion. The investigator studies thestability and instability of equilibria in fluids and plasmas. Mathematical advances here enhance our understanding of thephysical mechanisms that govern stability and instability, and socan lead to better numerical methods for simulations of thesecomplex phenomena. Fluid stability is important in understandingthe mechanisms of ocean waves and the movements of the atmosphereas well as in engineering applications. Questions of plasmastability arise in areas as diverse as sunspots, fundamentalplasma physics, the design of fusion machines, and plasma displaydevices.