[{"key":"dc.contributor.author","value":"Titi, Edriss","language":null},{"key":"dc.date.accessioned","value":"2021-06-18T05:00:54Z","language":null},{"key":"dc.date.available","value":"2021-06-18T08:09:32Z","language":null},{"key":"dc.date.issued","value":"2020-11-27T10:00","language":null},{"key":"dc.identifier.other","value":"BIRS-VIDEO-202011271000-Titi","language":null},{"key":"dc.identifier.other","value":"BIRS-VIDEO-20w5188-37398","language":null},{"key":"dc.identifier.uri","value":"http:\/\/hdl.handle.net\/2429\/78730","language":null},{"key":"dc.description.abstract","value":"The Navier-Stokes-Voigt model of\nviscoelastic incompressible fluid has been proposed as a\nregularization of the three-dimensional Navier-Stokes equations for\nthe purpose of direct numerical simulations. Besides the kinematic\nviscosity parameter, $\\nu>0$, this model possesses a regularizing\nparameter, $\\alpha> 0$, a given length scale parameter, so that\n$\\frac{\\alpha^2}{\\nu}$ is the relaxation time of the viscoelastic\nfluid.  In this talk I will derive several statistical properties of\nthe invariant measures associated with the solutions of the\nthree-dimensional Navier-Stokes-Voigt equations. Moreover, I will show\nthat, for fixed viscosity, $\\nu>0$, as the regularizing parameter\n$\\alpha$ tends to zero, there exists a subsequence of probability\ninvariant measures converging, in a suitable sense, to a strong\nstationary statistical solution of the three-dimensional\nNavier-Stokes equations, which is a regularized version of the\nnotion of stationary statistical solutions - a generalization of the\nconcept of invariant measure introduced and investigated by Foias.\nThis fact is also supported by numerical observations, which provides an\nadditional evidence that, for small values of the regularization\nparameter $\\alpha$, the Navier-Stokes-Voigt model can indeed be\nconsidered as a model to study the statistical properties of the\nthree-dimensional Navier-Stokes equations and turbulent flows via\ndirect numerical simulations.","language":null},{"key":"dc.format.extent","value":"25.0 minutes","language":null},{"key":"dc.format.mimetype","value":"video\/mp4","language":null},{"key":"dc.language.iso","value":"eng","language":null},{"key":"dc.publisher","value":"Banff International Research Station for Mathematical Innovation and Discovery","language":null},{"key":"dc.relation","value":"20w5188: Multiscale Models for Complex Fluids: Modeling and Analysis (Online)","language":null},{"key":"dc.relation.ispartofseries","value":"BIRS Workshop Lecture Videos (Banff, Alta)","language":null},{"key":"dc.rights","value":"Attribution-NonCommercial-NoDerivatives 4.0 International","language":null},{"key":"dc.rights.uri","value":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/","language":null},{"key":"dc.subject","value":"Mathematics","language":null},{"key":"dc.subject","value":"Partial Differential Equations","language":null},{"key":"dc.subject","value":"Fluid Mechanics","language":null},{"key":"dc.subject","value":"Fluid Dynamics","language":null},{"key":"dc.title","value":"Statistical Properties of the Navier-Stokes-Voigt Model","language":null},{"key":"dc.type","value":"Moving Image","language":null},{"key":"dc.description.affiliation","value":"Non UBC","language":null},{"key":"dc.description.reviewstatus","value":"Unreviewed","language":null},{"key":"dc.description.notes","value":"Author affiliation: Texas A&M University","language":null},{"key":"dc.description.scholarlevel","value":"Faculty","language":null},{"key":"dc.date.updated","value":"2021-06-18T05:00:54Z","language":null}]