发表机构
Clemson University; University of South Carolina（克莱姆森大学; 南卡罗来纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明二维原始方程在次临界水平耗散下对任意大初始数据全局适定，通过流体静力能量估计和涡度最大值原理确立尖锐耗散阈值。
AI 中文摘要
我们建立了具有分数阶水平耗散的二维原始方程在完整次临界范围 $1<\alpha\leq2$ 内、对任意大初始数据的经典解的全局适定性。结合已知的 $0\leq\alpha<1$ 的不适定性结果，这确立了相应解框架中大数据全局适定性的尖锐耗散阈值。关键要素是通过将非线性能量分解为对称和反对称部分，并利用后者的交换子结构，得到的一个流体静力能量估计。利用各向异性和不可压缩性，我们将非线性能量以流体静力涡度的 $L^\infty$ 范数乘以仅含额外半个水平导数的二次速度范数来界定。涡度最大值原理随后产生增强的速度界，这闭合了涡度估计，并在整个次临界范围内验证了延拓准则。
英文摘要
We establish global well-posedness of classical solutions to the two-dimensional primitive equations with fractional horizontal dissipation for arbitrarily large initial data in the full subcritical range $1<α\leq2$. Together with the known ill-posedness results for $0\leqα<1$, this establishes the sharp dissipation threshold for large-data global well-posedness in the corresponding solution framework. The key ingredient is a hydrostatic energy estimate obtained by splitting the nonlinear energy into symmetric and antisymmetric parts and exploiting the commutator structure of the latter. Using anisotropy and incompressibility, we bound the nonlinear energy by the $L^\infty$ norm of the hydrostatic vorticity times a quadratic velocity norm with only one-half additional horizontal derivative. The vorticity maximum principle then yields enhanced velocity bounds, which close the vorticity estimates and verify the continuation criterion throughout the subcritical regime.
Comments20 pages
