Seminar on Qualitative Theory of Differential Equations - Takayoshi Ogawa (11.10.2018)
Thursday 11.10.2018 at 14:00, Lecture room M/223
By: Pavol Quittner
Takayoshi Ogawa (Tohoku University):
Maximal regularity for the Cauchy problem of heat quations in BMO and its application
General theory of maximal regularity for the Cauchy problem of parabolic equations is well-established in the framework of UMD-Banach spaces. Since UMD-Banach space is necessarily reflexive, maximal regularity for any non-reflexive Banach space requires each consideration. We show maximal regularity for the Cauchy problem of heat equations in the space of BMO and show the sharp initial trace estimate. As an application, we extend the estimate into the Stokes system and apply some quasi-linear parabolic equation related to the MHD system.