Publications

Research interests

E. Deléage, “Hyperbolicity study of models for turbulent two-phase flows obtained from the variational principle” (2024) HAL _{Summary: In this work, I present new hyperbolic systems modeling two-phase flows. They are obtained from Hamilton’s principle. The novelty of this work is the presence of turbulence.}
E. Deléage, G.L. Richard “A depth-averaged model for granular flow consistent with the incompressible 𝜇(𝐼) rheology” (2024) HAL _{Summary: In this work, we derive a depth-averaged hyperbolic model for granular flow which is consistent with the 𝜇(𝐼) rheology. The three variables of the model are the height, the mean velocity, and the shear. The roll wave instability is studied and a good agreement with experimental data and with the theoretical predictions for the rheology is obtained.}
E. Deléage, M.A. Mehmood “Stability of partially congested travelling wave solutions for the extended Aw-Rascle system” (2024) HAL _{Summary: In this work, we prove the non-linear stability of travelling-wave solutions to the one dimensional compressible pressureless Navier-Stokes system with a singular diffusion coefficient. This singularity encodes congestion effects.}

E. Deléage “Well-posedness of Reynolds averaged equations for compressible fluids with a vanishing pressure” Mathematical Methods in the Applied Sciences, 2023, 47 (2), pp.817-824 HAL _{Summary: In this work, I show that Reynolds averaged equations for a turbulent barotropic flow are Friedrichs-symmetrizable if and only if the gradient of the pressure of the fluid vanishes.}
E. Deléage, F. Linares “Well-posedness for the initial value problem associated to the Zakharov–Kuznetsov (ZK) equation in asymmetric spaces” SN Partial Differential Equations and Applications, 2023, 4 (2), pp.9. HAL _{Summary: In this work, we show that the Zakharov-Kuznetsov equation is well-posed in asymmetric spaces, and that it has a regularizing effect in these spaces. This is a multi-dimensional extension of a similar result obtained by Kato for the Korteweg-de Vries equation.}