TY  - JOUR
A1  - Shlapunov, Alexander
A1  - Tarchanov, Nikolaj Nikolaevič
T1  - An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over R-n
JF  - Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija
N2  - We consider an initial problem for the Navier-Stokes type equations associated with the de Rham complex over R-n x[0, T], n >= 3, with a positive time T. We prove that the problem induces an open injective mappings on the scales of specially constructed function spaces of Bochner-Sobolev type. In particular, the corresponding statement on the intersection of these classes gives an open mapping theorem for smooth solutions to the Navier-Stokes equations.
KW  - Navier-Stokes equations
KW  - de Rham complex
KW  - open mapping theorem
Y1  - 2021
U6  - https://doi.org/10.33048/semi.2021.18.108
SN  - 1813-3304
VL  - 18
IS  - 2
SP  - 1433
EP  - 1466
PB  - Institut Matematiki Imeni S. L. Soboleva
CY  - Novosibirsk
ER  -