偏微分方程研讨班：Local well-posedness for two-phase fluid motion in Oberbeck-Boussinesq approximation

中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：张伟 博士 （首都师范大学）

题  目：Local well-posedness for two-phase fluid motion in Oberbeck-Boussinesq approximation

时  间：2022.12.19（星期一）10:00-11:00

地  点：腾讯会议：808-308-542  会议密码：221219

摘  要：In this talk, we will discuss the local well-posedness of the Oberbeck-Boussinesq approximation for the unsteady motion of a drop in another fluid separated by a closed interface with surface tension. First, we use the Hanzawa transformation to obtain the linearized Oberbeck-Boussinesq approximation in the fixed domain. Second, we prove the existence of $\mathcal{R}$-bounded solution operators for the model problems and the maximal $L^p-L^q$ regularity of the linearized Oberbeck-Boussinesq approximation. The key step is to prove the maximal $L^p-L^q$ regularity theorem for the linearized heat equation with the help of the $\mathcal{R}$-bounded solution operators for the corresponding resolvent problem and the Weis operator-valued Fourier multiplier theorem. Finally, we estimate the difference in nonlinear terms, after which the existence and uniqueness of the solutions are proven by the contraction mapping principle. The talk is based on joint work with Hao Chengchun.