Asymptotic behaviour of a rapidly rotating fluid with random stationary surface stress

Navier-Stokes equations on a rapidly rotating sphere

We extend our earlier β-plane results [al-Jaboori and Wirosoetisno, 2011, DCDS-B 16:687--701] to a rotating sphere. Specifically, we show that the solution of the Navier--Stokes equations on a sphere rotating with angular velocity 1/ε becomes zonal in the long time limit, in the sense that the non-zonal component of the energy becomes bounded by εM. We also show that the global attractor reduces to a single stable steady state when the rotation is fast enough.

无热扩散的三维快速旋转对流模型分析

Analysis of a three-dimensional rapidly rotating convection model without thermal diffusion

本文针对无热扩散的三维快速旋转对流模型，通过先研究带热扩散的正则化模型并建立与扩散系数无关的精细估计，证明了弱解的全局存在唯一性和强解的Hadamard适定性。

Rapidly Rotating White Dwarfs

A rotating star may be modeled as a continuous system of particles attracted to each other by gravity and with a given total mass and prescribed angular velocity. Mathematically this leads to the Euler-Poisson system. A white dwarf star is modeled by a very particular, and rather delicate, equation of state for the pressure as a function of the density. We prove an existence theorem for rapidly rotating white dwarfs that depend continuously on the speed of rotation. The key tool is global continuation theory, combined with a delicate limiting process. The solutions form a connected set $\mathc…

Rapidly Rotating Stars

A rotating star may be modeled as a continuous system of particles attracted to each other by gravity and with a given total mass and prescribed angular velocity. Mathematically this leads to the Euler-Poisson system. We prove an existence theorem for such stars that are rapidly rotating, depending continuously on the speed of rotation. This solves a problem that has been open since Lichtenstein's work in 1933. The key tool is global continuation theory, combined with a delicate limiting process. The solutions form a connected set $\mathcal K$ in an appropriate function space. As the speed of …

Global well-posedness for a rapidly rotating convection model of tall columnar structure in the limit of infinite Prandtl number

We analyze a three-dimensional rapidly rotating convection model of tall columnar structure in the limit of infinite Prandtl number, i.e., when the momentum diffusivity is much more dominant than the thermal diffusivity. Consequently, the dynamics of the velocity field takes place at a much faster time scale than the temperature fluctuation, and at the limit the velocity field formally adjusts instantaneously to the thermal fluctuation. We prove the global well-posedness of weak solutions and strong solutions to this model.

论单位圆盘中的快速旋转涡度

On the rapidly rotating vorticity in the unit disk

本文基于扰动方法，在单位圆盘中构造了具有充分大角速度的均匀旋转涡度解，揭示了高度旋转流体中微妙的多尺度现象。