On the stability phenomenon of the Navier-Stokes type equations for elliptic complexes : научное издание

Описание

Тип публикации: статья из журнала

Год издания: 2021

Идентификатор DOI: 10.1080/17476933.2020.1835877

Ключевые слова: navier-stokes type equations, elliptic complexes, holder spaces, 58j35, hölder spaces, primary: 76d05, secondary: 58j10

Аннотация: Let chi be a Riemannian n-dimensional smooth closed manifold, n >= 2, E-i be smooth vector bundles over chi and {A(i), E-i} be an elliptic differential complex of linear first order operators. We consider the operator equations, induced by the Navier-Stokes type equations associated with {A(i), E-i} on the scale of anisotropic HoldПоказать полностьюer spaces over the layer chi x [0, T] with finite time T > 0. Using the properties of the differentials A(i) and parabolic operators over this scale of spaces, we reduce the equations to a nonlinear Fredholm operator equation of the form (I + K)u = f, where K is a compact continuous operator. It appears that the Frechet derivative (I + K)' is continuously invertible at every point of each Banach space under consideration and the map (I + K) is open and injective in the space.

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Издание

Журнал: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS

Номера страниц: 1122-1150

ISSN журнала: 17476933

Место издания: ABINGDON

Издатель: TAYLOR & FRANCIS LTD

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