an:06033444
Zbl 1242.49063
Gigli, Nicola; Mosconi, Sunra J. N.
A variational approach to the Navier-Stokes equations
EN
Bull. Sci. Math. 136, No. 3, 256-276 (2012).
00299197
2012
j
49M25 35Q30 76Y05
Navier--Stokes equations; gradient flows; discretization; Leray/Hopf solutions; smallness condition
Summary: We propose a time discretization of the Navier--Stokes equations inspired by the theory of gradient flows. This discretization produces Leray/Hopf solutions in any dimension and suitable solutions in dimension 3. We also show that in dimension 3 and for initial data in \(H^{1}\), the scheme converges to strong solutions in some interval [0,T) and, if the data satisfy the classical smallness condition, it produces the smooth solution in [\(0,\infty \)).