Тип публикации: статья из журнала
Год издания: 2018
Идентификатор DOI: 10.17654/FM021020127
Ключевые слова: Navier-Stokes equations, Weighted hölder spaces, integral representation method
Аннотация: We consider the Navier-Stokes equations in the layer over with finite Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes equations to a nonlinear Fredholm equation of the form where K is a compact continuous operator in anisotropic normed Hölder spaces weighted atПоказать полностьюthe point at infinity with respect to the space variables. Actually, the weight function is included to provide a finite energy estimate for solutions to the Navier-Stokes equations for all On using the particular properties of the de Rham complex we conclude that the Fréchet derivative is continuously invertible at each point of the Banach space under consideration and the map is open and injective in the space. In this way, the Navier-Stokes equations prove to induce an open one-to-one mapping in the scale of Hölder spaces.
Журнал: Advances and Applications in Fluid Mechanics
Выпуск журнала: Т. 21, № 2
Номера страниц: 127-246
ISSN журнала: 09734686