A variational approach to Navier–Stokes. (15th November 2018)

• Record Type: Journal Article
• Authors: Ortiz, Michael; Schmidt, Bernd; Stefanelli, Ulisse
• Is Part Of: Nonlinearity. Volume 31:Number 12(2018:Dec.)
• Page Start: 5664
• Page End: 5682
• Publication Date: 2018-11-15
• Subjects: Navier–Stokes system -- variational method -- weak solutions -- weighted-inertia-dissipation-energy functionals; 35Q30 -- 76D05; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aae722
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: 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.