论文标题
与对称性的关键表面准斑块方程的非衰减解决方案
Non-decaying solutions to the critical surface quasi-geostrophic equations with symmetries
论文作者
论文摘要
我们开发了一种自相似解决方案的理论，用于关键的表面准地神经斑方程。我们为各种规律性类别中的任意大数据构建自相似的解决方案，并在小型数据制度，唯一性和全球渐近稳定性中证明。这些解决方案不偿还$ | x | \ to +\ infty $，导致速度$ \ vec {r}^\perpθ$中的歧义。通过强加$ m $折的旋转对称性来纠正这种歧义。这里展出的自相似解决方案就在于已知的良好的理论之外，并且有望阐明由于对称性的分叉，与工作\ cite \ cite {jiasverakillpposed，guillodsverak}相比，在Navier-Stokes方程式上。
We develop a theory of self-similar solutions to the critical surface quasi-geostrophic equations. We construct self-similar solutions for arbitrarily large data in various regularity classes and demonstrate, in the small data regime, uniqueness and global asymptotic stability. These solutions are non-decaying as $|x| \to +\infty$, which leads to ambiguity in the velocity $\vec{R}^\perp θ$. This ambiguity is corrected by imposing $m$-fold rotational symmetry. The self-similar solutions exhibited here lie just beyond the known well-posedness theory and are expected to shed light on potential non-uniqueness, due to symmetry-breaking bifurcations, in analogy with work \cite{jiasverakillposed,guillodsverak} on the Navier-Stokes equations.
