DOAJ Open Access 2022

Generalized Navier–Stokes Equations with Non-Homogeneous Boundary Conditions

Evgenii S. Baranovskii Mikhail A. Artemov

Abstrak

We study the generalized unsteady Navier–Stokes equations with a memory integral term under non-homogeneous Dirichlet boundary conditions. Using a suitable fractional Sobolev space for the boundary data, we introduce the concept of strong solutions. The global-in-time existence and uniqueness of a small-data strong solution is proved. For the proof of this result, we propose a new approach. Our approach is based on the operator treatment of the problem with the consequent application of a theorem on the local unique solvability of an operator equation involving an isomorphism between Banach spaces with continuously Fréchet differentiable perturbations.

Topik & Kata Kunci

Thermodynamics Mathematics Analysis

Penulis (2)

Evgenii S. Baranovskii

Mikhail A. Artemov

Format Sitasi

APA MLA BibTeX

Baranovskii, E.S., Artemov, M.A. (2022). Generalized Navier–Stokes Equations with Non-Homogeneous Boundary Conditions. https://doi.org/10.3390/fractalfract6070373

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Informasi Jurnal

Tahun Terbit: 2022
Sumber Database: DOAJ
DOI: 10.3390/fractalfract6070373
Akses: Open Access ✓