Time-Asymptotic Behavior of Incompressible Plasmas

Large time behavior in perfect incompressible flows

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On Asymptotic Behavior of Stopping Time Problems

Turbulent Cascades in 3d Incompressible Plasmas

This report surveys mathematical results related to plasma turbulence obtained while supported by the VSGC Graduate Research Fellowship. The solar-wind and interstellar medium are highly turbulent plasmas exhibiting certain features ubiquitous across present numerical and phenomenological theories. The objective of the present research is to provide a rigorous validation of such aspects of thes...

Asymptotic behavior of a suspension of oriented particles in a viscous incompressible fluid

Abstract. A viscous incompressible fluid with a large number of small axially symmetric solid particles is considered. It is assumed that the particles are identically oriented and under the influence of the fluid move translationally or rotate around a symmetry axis with the direction of their symmetry axes unchanged. The asymptotic behavior of oscillations of the system is studied, when the d...

On the asymptotic behavior of the equations describing the motion of an incompressible binary fluid

We determine the asymptotic behavior of the system of Cahn-Hillard/Euler's equations that control the dynamics inside the thin boundary layer separating two inviscid, incompressible, and nearly immiscible fluids. This model was proposed recently in order to replace the classical moving boundary model of two immiscible fluids, separated by the interface with the surface tension. We formally veri...