Joanna Renc?awowicz; Wojciech M. Zaj?czkowski The Large Flux Problem to the Navier-Stokes Equations 9783030323295

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Автор: Joanna Renc?awowicz; Wojciech M. Zaj?czkowski
Название: The Large Flux Problem to the Navier-Stokes Equations
ISBN: 9783030323295
Издательство: Springer
Классификация:

Функциональный анализ и преобразования

Дифференциальное исчисление и дифференциальные уравнения

Классическая механика

ISBN-10: 3030323293
Обложка/Формат: Soft cover
Страницы: 179
Вес: 0.30 кг.
Дата издания: 2019
Серия: Lecture Notes in Mathematical Fluid Mechanics
Язык: English
Издание: 1st ed. 2019
Иллюстрации: 1 illustrations, color; 2 illustrations, black and white; vi, 179 p. 3 illus., 1 illus. in color.
Размер: 234 x 156 x 10
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Подзаголовок: Global Strong Solutions in Cylindrical Domains
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: 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.
Дополнительное описание: Introduction.- Notation and auxiliary results.- Energy estimate: Global weak solutions.- Local estimates for regular solutions.- Global estimates for solutions to problem on (v, p).- Global estimates for solutions to problem on (h, q).- Estimates for ht.-

The Large Flux Problem to the Navier-Stokes Equations, Joanna Renc?awowicz; Wojciech M. Zaj?czkowski