发表机构
Nankai University; Nanchang University; Tiangong University（南开大学; 南昌大学; 天津工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究二维全局域中非齐次不可压缩Navier-Stokes系统，利用相消结构和Hardy空间估计，证明速度指数衰减及强解的全局适定性和流映射正则性。
AI 中文摘要
我们研究了二维全局域中具有零初始总动量的非齐次不可压缩Navier-Stokes系统，允许真空和具有有限矩但不一定紧支撑的密度。利用二维方程固有的相消结构以及密度的空间矩界，我们推导出惯性力属于Hardy空间，并通过端点Hardy-Littlewood-Sobolev不等式建立了加权Stokes估计。这些估计识别了远场速度并控制了余项，从而在整个全局域中实现速度的一致指数衰减。结合更高阶的正则性界，我们建立了密度依赖黏性情形下强解的全局适定性，并在常黏性模型中证明了可测密度斑块流映射的一致正则性。
英文摘要
We investigate the inhomogeneous incompressible Navier-Stokes system in the 2D global domain with zero initial total momentum, allowing vacuum and densities with finite moments but not necessarily compact support. Exploiting the cancellation structure inherent in the 2D equations along with spatial moment bounds on the density, we derive that the inertial force belongs to the Hardy space and establish weighted Stokes estimates through endpoint Hardy-Littlewood-Sobolev inequalities. These estimates identify the far-field velocity and control the remainder, leading to uniform exponential decay of the velocity throughout global domains. Combined with higher order regularity bounds, we establish the global well-posedness of strong solutions for the density-dependent viscosity case, and prove the uniform regularity of flow maps for measurable density patches in the constant viscosity model.
