The formation of strong and potentially singular fronts in a two-dimensional quasigeostrophic active scalar is studied through the symbiotic interaction of mathematical theory and numerical… Expand

We discuss necessary and sufficient conditions for the formation of finite time singularities (blow up) in the incompressible three dimensional Euler equations. The well-known result of Beale, Kato… Expand

The author presents results regarding certain average properties of incompressible fluids derived from the equations of motion, the average dissipation rate and the average dimension of level sets.Expand

Abstract Using a new version of the Sobolev-Lieb-Thirring inequality, we derive an upper bound for the dimension of the universal attractor for two-dimensional space periodic Navier-Stokes equations.… Expand

We study solutions to the 2D quasi-geostrophic (QGS) equation $$ \frac{\partial \theta}{\partial t}+u\cdot\nabla\theta + \kappa (-\Delta)^{\alpha}\theta=f $$ and prove global existence and uniqueness… Expand

We consider Navier-Stokes equations coupled to nonlinear FokkerPlanck equations describing the probability distribution of particles interacting with fluids. We describe relations determining the… Expand