On September 8, there was a math seminar by Dr. Ken Furukawa. He gave a talk entitled Maximal Regularity and Partial Differential Equations.

In the first part of his talk, the speaker explained the maximal regularity of parabolic partial differential equations and various sufficient conditions for the maximal regularity. Especially he introduced some functional calculus to obtain the analytic semigroup.

In the second part, the speaker explained his recent collaboration work on the primitive equation and its relationship to the Navier-Stokes equation. He first shows that we can formally obtain primitive equations from the Navier-Stokes equation on the thin domain. He then explained his recent collaboration work which justifies this formal derivation of the primitive equation and how the sufficient conditions in the first talk work.