The theory of homogeneous turbulence, Cambridge Monographs on Mechanics and Applied Mathematics, 1953. ,
Mathematics of Large Eddy Simulation of turbulent flows. Scientific Computation, 2006. ,
On the Reynolds time-averaged equations and the longtime behavior of Leray-Hopf weak solutions, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01695374
Suitable weak solutions of the Navier-Stokes equations constructed by a space-time numerical discretization, J. Math. Pures Appl, vol.125, issue.9, pp.189-208, 2019. ,
Mathematical and numerical foundations of turbulence models and applications. Modeling and Simulation in Science, Engineering and Technology, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01149312
Navier-Stokes equations, Chicago Lectures in Mathematics, 1988. ,
Intermodal energy transfers in a proper orthogonal decomposition-Galerkin representation of a turbulent separated flow, J. Fluid Mech, vol.491, pp.275-284, 2003. ,
A conservative, second order, unconditionally stable artificial compression method, Comput. Methods Appl. Mech. Engrg, vol.325, pp.733-747, 2017. ,
An artificial compression reduced order model, 2019. ,
Finite element methods for Navier-Stokes equations, Springer Series in Computational Mathematics, 1986. ,
/73) Statistical study of Navier-Stokes equations, I, II. Rend. Sem. Mat. Univ. Padova, vol.48, pp.9-123, 1972. ,
Navier-Stokes equations and turbulence, of Encyclopedia of Mathematics and its Applications, vol.83, 2001. ,
An overview of projection methods for incompressible flows, Comput. Methods Appl. Mech. Engrg, vol.195, pp.6011-6045, 2006. ,
Mathematical perspectives on large eddy simulation models for turbulent flows, J. Math. Fluid Mech, vol.6, issue.2, pp.194-248, 2004. ,
Certified reduced basis methods for parametrized partial differential equations, BCAM Basque Center for Applied Mathematics, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01223456
Are the snapshot difference quotients needed in the proper orthogonal decomposition? SIAM, J. Sci. Comput, vol.36, issue.3, pp.1221-1250, 2014. ,
Algorithms and models for turbulence not at statistical equilibrium, Comput. Math. Appl, vol.71, issue.11, pp.2352-2372, 2016. ,
The local structure of turbulence in incompressible viscous fluids for very large Reynolds number, Dokl. Akad. Nauk SSR, vol.30, pp.9-13, 1941. ,
Model order reduction in fluid dynamics: challenges and perspectives, Reduced order methods for modeling and computational reduction, vol.9, pp.235-273, 2014. ,
The 1877 Boussinesq conjecture: Turbulent fluctuations are dissipative on the mean flow, 2014. ,
Approximate Deconvolution Models of Turbulence Approximate Deconvolution Models of Turbulence, Lecture Notes in Mathematics, vol.2042, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00003252
Long-time turbulence model deduced from the Navier-Stokes equations, Chin. Ann. Math. Ser. B, vol.36, issue.5, pp.883-894, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01192773
Quelques méthodes de résolution des problèmes aux limites non linéaires, 1969. ,
Weak and Measure-valued Solutions to Evolutionary PDEs, Applied Mathematics and Mathematical Computations, vol.13, 1996. ,
Berichtüber Untersuchungen zur ausgebildeten Turbulenz, Z. Angew. Math. Mech, vol.5, pp.136-139, 1925. ,
Teoremi ergodici per le equazioni della idrodinamica, 1960. ,
On probability measures related to the Navier-Stokes equations in the 3-dimensional case, Univ. Trieste. Air Force Res. Div. Contract, vol.61, pp.52-414, 1961. ,
Reduced basis methods for partial differential equations, vol.92, 2016. ,
Certified reduced basis approximation for parametrized partial differential equations and applications, J. Math. Ind, vol.1, issue.3, p.44, 2011. ,
On the dynamic theory of the incompressible viscous fluids and the determination of the criterion, Philos. Trans. Roy. Soc. London Ser. A, vol.186, pp.123-164, 1895. ,
Fundamentals of reduced basis method for problems governed by parametrized PDEs and applications, Separated representations and PGD-based model reduction, vol.554, pp.153-227, 2014. ,
Large eddy simulation for incompressible flows. Scientific Computation, 2001. ,
An evolve-then-filter regularized reduced order model for convection-dominated flows, Internat. J. Numer. Methods Fluids, vol.84, issue.10, pp.598-615, 2017. ,
Approximate deconvolution reduced order modeling, Comput. Methods Appl. Mech. Engrg, vol.313, pp.512-534, 2017. ,
Data-driven filtered reduced order modeling of fluid flows, SIAM J. Sci. Comput, vol.40, issue.3, pp.834-857, 2018. ,
Lagrangian data-driven reduced order modeling of finite time Lyapunov exponents, the Author(s), 2018. ,