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方程在活动标量θ下的封闭水平集.在对上述水平集满足简单的几何条件并且⊥θ的大小沿着水平集与Ω(t)可比的情况下,证明了有限时间的非爆炸性.

The dynamic evolution of a closed level set of the active scalar 0 in the 2D quasi-geostrophic（QG） equation is studied. Under some mild assumptions about the geometry of the level set and the magnitude of △⊥θ along the level set, the nonexistence of finite-time blowup for the 2D QG equation is obtained.