On 3D Navier–Stokes equations: Regularization and uniqueness by delays
Article
Bessaih, H, Garrido-Atienza, MJ, Schmalfuß, B. (2018). On 3D Navier–Stokes equations: Regularization and uniqueness by delays
. PHYSICA D-NONLINEAR PHENOMENA, 376-377 228-237. 10.1016/j.physd.2018.03.004
Bessaih, H, Garrido-Atienza, MJ, Schmalfuß, B. (2018). On 3D Navier–Stokes equations: Regularization and uniqueness by delays
. PHYSICA D-NONLINEAR PHENOMENA, 376-377 228-237. 10.1016/j.physd.2018.03.004
A modified version of the three dimensional Navier–Stokes equations is considered with periodic boundary conditions. A bounded constant delay is introduced into the convective term, that produces a regularizing effect on the solution. In fact, by assuming appropriate regularity on the initial data, the solutions of the delayed equations are proved to be regular and, as a consequence, existence and also uniqueness of a global weak solution are obtained. Moreover, the associated flow is constructed and the continuity of the semigroup is proved. Finally, we investigate the passage to the limit on the delay, obtaining that the limit is a weak solution of the Navier–Stokes equations.
