A variational approach to Navier-Stokes
We present a variational resolution of the incompressible Navier–Stokes system by means of stabilized weighted-inertia-dissipation-energy (WIDE) functionals. The minimization of these parameter-dependent functionals corresponds to an elliptic-in-time regularization of the system. By passing to the limit in the regularization parameter along subsequences of WIDE minimizers one recovers a classical Leray–Hopf weak solution.
© 2018 IOP Publishing Ltd & London Mathematical Society. Received 19 February 2018; Accepted 10 October 2018; Published 15 November 2018. U.S. is partly funded by the Vienna Science and Technology Fund (WWTF) through Project MA14-009 and by the Austrian Science Fund (FWF) projects F 65, P 27052, and I 2375.
Submitted - 1802.06606.pdf