engleski

A parabolic variant of H-measures

H-measures, as originally introduced by Luc Tartar and (independently) Patrick G\'erard are well suited for hyperbolic problems. For parabolic problems, some variants should be considered, which would be better addapted to parabolic problems. We shall present a parabolic scaling and a particular variant, together with a number of examples. The main ingredients of the proofs will be given, in comparison to to the original H-measures. In particular, the first commutation lemma will be discussed. As for the classical H-measures, a natural step is to investigate localisation and propagation properties. For the first, a particular anysotropic Sobolev space will be defined, which is needed for the statement of the localisation property. First results for the latter property will be given in the talk by Martin Lazar. Finally, an application in homogenisation will be given, for a model based on the Stokes system.

H-measure; parabolic equation; turbulence; homogenisation; linearised Navier-Stokes system

nije evidentirano