流体数学セミナー

第 17 回　流体数学セミナー

日　時: 2025 年4月25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:　高橋知希氏(神奈川大学工学部)
講演題目: Spatial pointwise behavior of gradient of Navier-Stokes flow around a rigid body moving by time-periodic motion, with applications to stability/attainability of time periodic flow
講演要旨: We consider the spatial pointwise behavior of the Navier-Stokes liquid
around a rigid body, moving by time-periodic motion. For the translational and angular velocity of a body, assuming besides smallness and regularity, either of the following conditions: (i) translation or rotation is absent; (ii) both velocities are parallel to the same constant vector. If time average over a period of translational velocity, ζ (say), is nonzero (resp. zero), we then show that gradient of the velocity of the fluid decays like the one of the Oseen fundamental solution (resp. decays at the rate O(|x|^{-2})). Those estimates lead to the summability properties of the velocity field, which play an important role to understand the large time behavior of unsteady flows through stability/attainability analysis of the related time periodic ones. To see this issue, we will provide new results in the following two settings: stability analysis in the case of (ii) with nonzero $\zeta$; attainability analysis in the rotational case.

日　時: 2025 年 5 月 9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:　中里亮介氏(信州大学)
講演題目:　Analyticity and its application to the solution of compressible Navier-Stokes-Korteweg equations with zero sound speed in scaling critical framewor
講演要旨: We consider the initial-value problem for the compressible Navier-Stokes-Korteweg equations in the d-dimensional Euclidean space R^d (d≧3).The system is well-known as the Diffuse Interface model describing the motion of a vaper-liquid mixture in a compressible viscous fluid. In this talk, we would like to handle the analyticity and time-decay estimates of the global-in-time solution around the constant equilibrium states (ρ_*,0) (ρ_*>0) of the problem under the zero sound speed case (namely, P'(ρ_*)=0, where P=P(ρ) stands for the pressure) and scaling critical settings based on Fourier-Herz spaces. If time allows, we would introduce the result on the decay estimate of the first order asymptotic formula.This talk is based on the joint work with Prof. Takayuki Kobayashi (Osaka University).

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