The Large Flux Problem to the Navier-Stokes Equations:Global Strong Solutions in Cylindrical Domains(Lecture Notes in Mathematical Fluid Mechanics)

纳维-斯托克斯方程的大通量问题:圆柱领域的全球强大解决方案

偏微分方程

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879.00
发货周期:预计8-10周发货
作      者
出版时间
2019年10月12日
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平装
ISBN
9783030323295
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页      码
179
语      种
英文
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This monograph considers the motion of incompressible fluids described by the Navier-Stokes equations with large inflow and outflow, and proves the existence of global regular solutions without any restrictions on the magnitude of the initial velocity, the external force, or the flux. To accomplish this, some assumptions are necessary: The flux is close to homogeneous, and the initial velocity and the external force do not change too much along the axis of the cylinder. This is achieved by utilizing a sophisticated method of deriving energy type estimates for weak solutions and global estimates for regular solutions—an approach that is wholly unique within the existing literature on the Navier-Stokes equations. To demonstrate these results, three main steps are followed: first, the existence of weak solutions is shown; next, the conditions guaranteeing the regularity of weak solutions are presented; and, lastly, global regular solutions are proven. This volume is ideal for mathematicians whose work involves the Navier-Stokes equations, and, more broadly, researchers studying fluid mechanics.
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