@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}
}
@article{MeraStepanenkoTarkhanov2018,
  author    = {Mera, Azal and Stepanenko, Vitaly A. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Successive approximation for the inhomogeneous burgers equation},
  series = {Journal of Siberian Federal University : Mathematics \& Physics},
  volume    = {11},
  journal   = {Journal of Siberian Federal University : Mathematics \& Physics},
  number    = {4},
  publisher = {Siberian Federal University},
  address   = {Krasnoyarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2018-11-4-519-531},
  pages     = {519 -- 531},
  year      = {2018},
  abstract  = {The inhomogeneous Burgers equation is a simple form of the Navier-Stokes equations. From the analytical point of view, the inhomogeneous form is poorly studied, the complete analytical solution depending closely on the form of the nonhomogeneous term.},
  language  = {en}
}
@article{MeraShlapunovTarkhanov2019,
  author    = {Mera, Azal and Shlapunov, Alexander A. and Tarkhanov, Nikolai Nikolaevich},
  title     = {Navier-Stokes Equations for Elliptic Complexes},
  series = {Journal of Siberian Federal University. Mathematics \& Physics},
  volume    = {12},
  journal   = {Journal of Siberian Federal University. Mathematics \& Physics},
  number    = {1},
  publisher = {Sibirskij Federalʹnyj Universitet},
  address   = {Krasnojarsk},
  issn      = {1997-1397},
  doi       = {10.17516/1997-1397-2019-12-1-3-27},
  pages     = {3 -- 27},
  year      = {2019},
  abstract  = {We continue our study of invariant forms of the classical equations of mathematical physics, such as the Maxwell equations or the Lam´e system, on manifold with boundary. To this end we interpret them in terms of the de Rham complex at a certain step. On using the structure of the complex we get an insight to predict a degeneracy deeply encoded in the equations. In the present paper we develop an invariant approach to the classical Navier-Stokes equations.},
  language  = {en}
}