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.

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.

Détail

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

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