Seminar

November 4, 11, 18, 25 (Thu) 14:00 -16:00 (Japan time)

Online (ZOOM)

Takayoshi Ogawa (Tohoku University, Research Alliance Center of Mathematical Sciences/Mathematical Institute)

Maxmal regularity for the heat and the Stokes equations in the class of bounded mean oscillations and related topics

I would like to talk on the outlined theory of maximal regularity on the simplest parabolic equations such as the heat equation and the Stokes equations in the limiting function class BMO (bounded mean oscillations). Maximal regularity for the Cauchy problem of parabolic equations is well-understood in the UMD Banach spaces. if the Banach space is UMD, then it is necessarily reflexive, Maximal regularity in non-reflexive space is exceptional case and it is required for an individual treatment to establish a related estimate. After introducing some basic facts on the functions in BMO, I will show maximal regularity holds for the solution to the Cauchy problem of the heat equation and the Stokes equations in BMO space. This talk is based on the joint work with Senjo Shimizu (Kyoto University).