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Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar
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 numericalExpand
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Geometric constraints on potentially singular solutions for the 3-D Euler equations
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, KatoExpand
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Global regularity for vortex patches
We present a proof of Chemin's [4] result which states that the boundary of a vortex patch remains smooth for all time if it is initially smooth.
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Geometric Statistics in Turbulence
TLDR
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
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On the dimension of the attractors in two-dimensional turbulence
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
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Behavior of solutions of 2D quasi-geostrophic equations
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 uniquenessExpand
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Nonlinear Fokker-Planck Navier-Stokes systems
We consider Navier-Stokes equations coupled to nonlinear FokkerPlanck equations describing the probability distribution of particles interacting with fluids. We describe relations determining theExpand
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