Author:
Fereidooni Amin,Moameni Abbas,Grewal Anant
Abstract
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.
Reference19 articles.
1. Charles J. Amick; Existence of solutions to the nonhomogeneous steady Navier-Stokes equations, Indiana University mathematics journal, 33 (1984), no. 6, 817-830. https://doi.org/10.21236/ADA129171
2. W. Borchers, K. Pileckas; Note on the flux problem for stationary incompressible Navier- Stokes equations in domains with a multiply connected boundary, Acta Applicandae Mathematica, 37 (1994), no. 1, 21-30. https://doi.org/10.1007/BF00995126
3. Haim Brézis, Lous Nirenberg, Guido Stampacchia; A remark on Ky Fan's minimax principle, Boll. Un. Mat. Ital, 6 (1972), no. 4, 293-300.
4. Robert Finn; On the steady-state solutions of the Navier-Stokes equations, iii, Acta Mathematica 105 (1961), no. 3-4, 197-244. https://doi.org/10.1007/BF02559590
5. H. Fujita; On stationary solutions to Navier-Stokes equation in symmetric plane domains under general outflow condition, Pitman Research Notes in Mathematics Series (1998), 16-30.