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.
Журнал: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
Номера страниц: 1122-1150
ISSN журнала: 17476933
Место издания: ABINGDON
Издатель: TAYLOR & FRANCIS LTD