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ustv imath

Group IMATH (Institut Mathématiques de Toulon, EA2134)

 Research topics
  • The realization of the theoretical part part of the ModTerCom project relies essentially on the members of the of the IMATH group: Khaled Bahlali, Gloria Faccanoni, Mehmet Ersoy, Cédric Galusinski, Antonin Novotny. K. Bahlali is specialist in stochastic partial differential equations, the main interests of G. Facannoni, M. Ersoy, C. Galusinski and A. Novotny is the analysis of partial differential equations especially the applications to fluid mechanics and thermodynamics.
  • The main objectives of this team will be to investigate various aspects of the relative entropy functional for the Navier-Stokes and Navier-Stokes-Fourier system: 1) Stability and weak strong uniqueness of the class of weak solutions in the class of strong solutions and in some weaker classes than strong solutions (as e.g. the Hoff class). 2) Establishing the relative entropy inequality for solutions of convergent numerical schemes for compressible Navier-Stokes equations. 3) Investigation of the effect of the driving forces of very low regularity with respect to time and of the stability of small stochastic perturbations of deterministic driving forces. 4) Multiscale analysis and model reduction of the Navier-Stokes-Fourier system with the focus to applications to geophysical and environmental flows. We name here some of the limits that have been studied in this situation: a) passage from compressible to incompressible fuid flows (low Mach number limit); b) passage from isotropic to anelastic flows (low Froude number limit); c) passage from rotating 3D flows to planar flows (low Rossby number limit); d) passage from viscous to inviscid flows (high Reynolds number limit). Physically realistic regimes are however usually characterized by a simultaneous action of several parameters entering into the game and tending to extreme values (zero or infinity) in a particular mutual rate. We shall concentrate to several physically interesting singular regimes of this type.
  • Problems related to item 2) will be investigated in the close collaboration with the LATP group. Formulation of the multiscale singular limits problems requiers the expertize of our colleagues from the MIO group. The theses of David Maltese co-supervised by Thierry Gallouet and Antonin Novotny will address the problems within the items 1), 2) and 4).