Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations
Thursday 11.10.2018 at 14:00 Lecture room M-223
Takayoshi Ogawa (Tohoku University):
Maximal regularity for the Cauchy problem of heat equations
in BMO and its application
and
Masaki Kurokiba (Muroran Institute of Technology):
Singular limit problem for the Keller-Segel system
to a drift-diffusion system in critical spaces
Abstracts:
T. Ogawa:
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.
M. Kurokiba:
We consider the singular limit problem of the Cauchy problem
for the Keller-Segel problem in the critical function spaces.
It is shown that the solution to the Keller-Segel system
in the scaling critical function spaces converges to the
solution to the drift-diffusion system of parabolic-elliptic
equations (simplified Keller-Segel model) in the critical space
strongly as a relaxation time parameter goes to infinity.
For the proof, we employ generalized maximal regularity for
heat equations and use it systematically with the sequence of
embeddings between the interpolation spaces.