Functional and generalized separable solutions to unsteady Navier-Stokes equations

Polyanin, A.D.; Zhurov, A.I.

Статья опубликована в высокорейтинговом журнале

Информация о цитировании статьи получена из Web of Science, Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 26 марта 2018 г.

Авторы: Polyanin A.D., Zhurov A.I.
Журнал: International Journal of Non-Linear Mechanics
Том: 79
Год издания: 2016
Издательство: Pergamon Press Ltd.
Местоположение издательства: United Kingdom
Первая страница: 88
Последняя страница: 98
DOI: 10.1016/j.ijnonlinmec.2015.10.015
Аннотация: The paper studies unsteady Navier-Stokes equations with two space variables. It shows that the nonlinear fourth-order equation for the stream function with three independent variables admits functional separable solutions described by a system of three partial differential equations with two independent variables. The system is found to have a number of exact solutions, which generate new classes of exact solutions to the Navier-Stokes equations. All these solutions involve two or more arbitrary functions of a single argument as well as a few free parameters. Many of the solutions are expressed in terms of elementary functions, provided that the arbitrary functions are also elementary; such solutions, having relatively simple form and presenting significant arbitrariness, can be especially useful for solving certain model problems and testing numerical and approximate analytical hydrodynamic methods. The paper uses the obtained results to describe some model unsteady flows of viscous incompressible fluids, including flows through a strip with permeable walls, flows through a strip with extrusion at the boundaries, flows onto a shrinking plane, and others. Some blow-up modes, which correspond to singular solutions, are discussed.

	ИСТИНА	Войти в систему Регистрация
	ИПМех РАН
	Главная Поиск Статистика О проекте Помощь

ИСТИНА

ИПМех РАН

Functional and generalized separable solutions to unsteady Navier-Stokes equationsстатья

Прикрепленные файлы