Electron. J. Differential Equations, Vol. 2023 (2023), No. 26, pp. 1-11.

Existence of solutions to steady Navier-Stokes equations via a minimax approach

Amin Fereidooni, Abbas Moameni, Anant Grewal

Our objective in this paper is to develop and utilize a minimax principle for proving the existence of symmetric solutions for the stationary Navier-Stokes equations. Notwithstanding its application to symmetric solutions in this paper, our minimax principle is broad enough to capture other types of solutions provided the equation and the external force are compatible under a family of operations including but not limited to being invariant by compact groups. The subset of functions compatible under this family of operations is not required to be a linear subspace, and being a closed convex set suffices for our purpose.

Submitted August 14, 2022. Published March 7, 2023.
Math Subject Classifications: 35Q30, 37K58.
Key Words: Navier-Stokes equations; variational principles.
DOI: https://doi.org/10.58997/ejde.2023.26

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Amin Fereidooni
National Research Council Canada
Ottawa, ON, Canada
email: Amin.Fereidooni@nrc-cnrc.gc.ca
Abbas Moameni
School of Mathematics and Statistics
Carleton University
Ottawa, ON, Canada
email: momeni@math.carleton.ca
Anant Grewal
National Research Council Canada
Ottawa, ON, Canada
email: Anant.Grewal@nrc-cnrc.gc.ca

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