An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over ${\mathbb R}^n$

A. A. Shlapunov; N. Tarkhanov

Geodesic

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An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over ${\mathbb R}^n$

A. A. Shlapunov ; N. Tarkhanov

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1433-1466

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Résumé

We consider an initial problem for the Navier-Stokes type equations associated with the de Rham complex over ${\mathbb R}^n \times [0,T]$, $n\geq 3$, 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.

Keywords: Navier-Stokes equations, de Rham complex, open mapping theorem.

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     author = {A. A. Shlapunov and N. Tarkhanov},
     title = {An open mapping theorem for the {Navier-Stokes} type equations associated with the de {Rham} complex over ${\mathbb R}^n$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1433--1466},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a72/}
}

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A. A. Shlapunov; N. Tarkhanov. An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over ${\mathbb R}^n$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 1433-1466. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a72/