论文标题
在尖锐的前部和几乎偏头的前部，用于单数平方英
On Sharp Fronts and Almost-Sharp Fronts for singular SQG
论文作者
论文摘要
在本文中，我们考虑一个由$ u =λ^{ - 1+α} \ nabla^{\ perp}θ$给出的活性标量的家族，用于$α\ in（0,1）$。这个方程家族是二维表面准地藻（SQG）方程的更为单数版本，它对应于$α= 0 $。 我们通过研究几乎出现的阵线的家庭来考虑锋利的战线的演变。这些是带有简单几何形状的平滑溶液，其中溶液中的急剧过渡发生在管状邻域（大小$δ$）中。我们研究了它们的演变和兼容曲线的演变，并引入了脊柱的概念，与其他兼容曲线相比，我们获得了改善的进化结果，获得了（$δ$）的全功率。
In this paper we consider a family of active scalars with a velocity field given by $u = Λ^{-1+α}\nabla^{\perp} θ$, for $α\in (0,1)$. This family of equations is a more singular version of the two-dimensional Surface Quasi-Geostrophic (SQG) equation, which would correspond to $α=0$. We consider the evolution of sharp fronts by studying families of almost-sharp fronts. These are smooth solutions with simple geometry in which a sharp transition in the solution occurs in a tubular neighbourhood (of size $δ$). We study their evolution and that of compatible curves, and introduce the notion of a spine for which we obtain improved evolution results, gaining a full power (of $δ$) compared to other compatible curves.
