论文标题
局部存在分析尖锐的奇异方面
Local Existence of Analytic Sharp Fronts for Singular SQG
论文作者
论文摘要
在本文中，我们通过使用抽象的cauchy -kowalevskaya定理证明了对广义SQG方程的分析尖锐解决方案的局部存在和独特性。在这里，速度由$ u = | \ nabla |^{ - 2β} \ nabla^\perpθ$（对于$ 1 <β\ leq 2 $）比在sqg中更为单数。尽管以合适的积分形式重塑了我们的方程式，但尽管出现了高于我们方程中一个高于一个方程的阶数值运算符，但这仍然可以实现。我们还提供了我们使用的Cauchy-Kowalevskaya定理的抽象版本的完整证明。
In this paper, we prove local existence and uniqueness of analytic sharp-front solutions to a generalised SQG equation by the use of an abstract Cauchy--Kowalevskaya theorem. Here, the velocity is determined by $u = |\nabla|^{-2β}\nabla^\perpθ$ which (for $1<β\leq 2$) is more singular than in SQG. This is achieved despite the appearance of pseudodifferential operators of order higher than one in our equation, by recasting our equation in a suitable integral form. We also provide a full proof of the abstract version of the Cauchy--Kowalevskaya theorem we use.
