二维quasi-geostrophic方程的几何结构和非爆炸性(英文)

Geometric Structure and Non-blowup of 2D Quasi-geostrophic Equation

讨论了二维quasi-geostrophic方程中的主动标量θ的封闭水平集C的动态演变.当水平集具有某种指定几何性质,那么在水平集上▽⊥θ的大小与Ω(t)可比的假设下,证明了有限时间T内解爆炸的不存在性.最后给出了一个2D QG方程的Lax对表示.

The dynamic evolution of a closed level set C of active scalar θ in the 2D quasi-geostrophic equation is studied. Under some mild assumptions about the geometry of the level set and with the condition that the magnitude of ▽⊥θ along C is comparable to Ω（t）, it is shown that there is no finite-time blowup up to time T. Later, in order to further analyze 2D QG equation, a Lax pair representation （L,A） of the equation is discussed.