This research school focuses on the mathematical study and analysis of geophysical fluid models. The field has seen many scientific activities in the last years since these equations form a basis e.g., for climate models. As in the case of the Navier-Stokes equations, many of these systems still lack, however, basic understanding concerning global existence and uniqueness of smooth solutions. In ocean and atmospheric dynamics, and also in the theory of boundary layers, one is hence investigating often reduced simplified models, whose derivations are based on formal asymptotic procedures, some of which are not systematic and calling for rigorous validation at the relevant temporal scales. These simplified models bring up difficult questions concerning well-posedness, validity, stability and also numerical approximations of these models.
Topics to be addressed in the school will include:
• global regularity and blow up, free boundary value problems, geophysical fluid structure interaction for viscous/inviscid compressible/incompressible equations subject to hydrostatic balance, e.g., the primitive equations of oceanic and atmospheric dynamics
• sea–ice models within the framework of scaling invariant spaces and thermodynamical consistency,
• multiphysics effects as moisture, vapour, phase transitions, interfaces, boundary layers, stratification and mixtures,
• existence or not of smoothing or dispersion effects due to noise and Coriolis forces,
• stability analysis of boundary layers and their inviscid limits,
• Prandtl’s equation,
• Rigorous justification of the hydrostatic approximation.
SPEAKERS (list tba)
SPONSORS OF THIS SEMESTER (to be completed)