论文标题
广义表面准地藻方程的自相似螺旋
Self-similar spirals for the generalized surface quasi-geostrophic equations
论文作者
论文摘要
在本文中，我们构建了一大批广义表面准地藻方程（GSQG）的非平凡（非辐射）自相似解。据我们所知，这是对这些方程式的任何相似解决方案的第一个严格结构。这些解决方案是螺旋型，可局部集成的，并且可能具有混合的符号。此外，它们与Scott和Dritschel在数值上的有限时间奇异性场景中具有一定的相似之处[R. K. Scott，D。G. Dritschel，《流体力学杂志》，863：R2，2019年]，在SQG贴片设置中。
In this paper we construct a large class of non-trivial (non-radial) self-similar solutions of the generalized surface quasi-geostrophic equation (gSQG). To the best of our knowledge, this is the first rigorous construction of any self-similar solution for these equations. The solutions are of spiral type, locally integrable, and may have mixed sign. Moreover, they bear some resemblance with the finite time singularity scenario numerically proposed by Scott and Dritschel [R. K. Scott, D. G. Dritschel., Journal of Fluid Mechanics, 863:R2, 2019] in the SQG patch setting.
