Тип публикации: препринт
Год издания: 2021
Идентификатор DOI: 10.48550/arXiv.2106.07515
Аннотация: We consider the initial problem for the Navier-Stokes equations over R3×[0, T] with a positive time T in the spatially periodic setting. Identifying periodic vector-valued functions on R3 with functions on the 3 -dimensional torus T 3 , we prove that the problem induces an open injective mapping As : Bs 1 → B s−1 2 where Bs 1 , B sПоказать полностью−1 2 are elements from scales of specially constructed function spaces of Bochner-Sobolev type parametrized with the smoothness index s ∈ N. Finally, we prove rather expectable statement that a map As is surjective if and only if the inverse image A −1 s (K) of any precompact set K from the range of the map As is bounded in the Bochner space Ls ([0, T], Ls (T 3 )) with the Ladyzhenskaya-Prodi-Serrin numbers s, r
Место издания: arXiv