Endpoint maximal regularity in BMO and its application to fluid mechanics
Appears in collection : Mathematics of fluids in motion: Recent results and trends / Fluides en mouvement : résultats récents et perspectives
We consider maximal regularity for the heat equation based on the endpoint function class BMO (the class of bounded mean oscillation). It is well known that BM O(Rn) is the endpoint class for solving the initial value problem for the incompressible Navier-Stokes equations and it is well suitable for solving such a problem ([3]) rather than the end-point homogeneous Besov spaces (cf. [1], [5]). First we recall basic properties of the function space BM O and show maximal regularity for the initial value problem of the Stokes equations ([4]). As an application, we consider the local well-posedness issue for the MHD equations with the Hall effect (cf. [2]). This talk is based on a joint work with Senjo Shimizu (Kyoto University).
