流体数学セミナー

第 24 回　流体数学セミナー

日　時: 2025 年 12 月 12日(金) 14時15分～ 15時15分
場所・教室:　お茶の水女子大学理学部1号館633教室
講演者:　Daniele Barbera 氏 (Politecnico di Torino)
講演題目:　Local existence through an energy method approach for
the Beris-Edwards model for liquid crystals
講演要旨:　In this talk, we consider the Beris-Edwards model for nematic liquid crystals, a state of matter intermediate between the solid state and the liquid state. In some previous works, it has been proved the Lp – Lq maximal regularity for the system in R^N and R^N+ . Generally, the local well-posedness of the problem is a consequence of such estimates. However, in the Beris-Edwards model the nonlinearities involve high order derivatives of the functions that prevents from applying a standard contraction argument. In the talk we show that, using an energy method approach and the structure of the problem in three dimensions, it is possible to get some cancellations of the high order terms and prove the local existence of the solution in the L2 setting. The seminar is based on a joint work with V. Georgiev, M. Murata and Y. Shibata.

日　時: 2025 年 12 月 12日(金) 15時30分～ 17時
場所・教室:　お茶の水女子大学理学部1号館633教室
講演者:　野ヶ山徹氏 (東京理科大学)
講演題目:　Maximal regularity estimates for heat equations on Besov spaces associated with Banach function spaces
講演要旨:
In this talk, we discuss the maximal regularity estimates for heat equations on the Besov spaces associated with ball Banach function spaces $\dot{B}^s_{X, r}$. Here, $X$ is a ball Banach function space.

It provides a general framework that includes many classical examples.

For example, if we take $X=L^p$, then we recover the classical homogeneous Besov space, and if we take $X={\mathcal M}^p_q$ (Morrey spaces), we obtain Besov—Morrey spaces.

To derive maximal regularity estimates, there are some general theories for Banach spaces with the UMD property. However, non-reflexive function spaces such as Morrey spaces don’t have the UMD property, so the general theory cannot be applied in this settings.

In this talk, we introduce the maximal regularity estimates for Besov type spaces which include non-UMD function spaces.

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流体数学セミナー　世話人