@article{MalassTarkhanov2020,
  author    = {Malass, Ihsane and Tarkhanov, Nikolaj Nikolaevič},
  title     = {A perturbation of the de Rham complex},
  series = {Journal of Siberian Federal University : Mathematics \& Physics},
  volume    = {13},
  journal   = {Journal of Siberian Federal University : Mathematics \& Physics},
  number    = {5},
  publisher = {Siberian Federal University},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2020-13-5-519-532},
  pages     = {519 -- 532},
  year      = {2020},
  abstract  = {We consider a perturbation of the de Rham complex on a compact manifold with boundary. This perturbation goes beyond the framework of complexes, and so cohomology does not apply to it. On the other hand, its curvature is "small", hence there is a natural way to introduce an Euler characteristic and develop a Lefschetz theory for the perturbation. This work is intended as an attempt to develop a cohomology theory for arbitrary sequences of linear mappings.},
  language  = {en}
}
@article{ShlapunovTarchanov2021,
  author    = {Shlapunov, Alexander and Tarchanov, Nikolaj Nikolaevič},
  title     = {An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over R-n},
  series = {Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija},
  volume    = {18},
  journal   = {Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija},
  number    = {2},
  publisher = {Institut Matematiki Imeni S. L. Soboleva},
  address   = {Novosibirsk},
  issn      = {1813-3304},
  doi       = {10.33048/semi.2021.18.108},
  pages     = {1433 -- 1466},
  year      = {2021},
  abstract  = {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.},
  language  = {en}
}