Large-Time Behavior of a Rigid Body of Arbitrary Shape in a Viscous Fluid Under the Action of Prescribed Forces and Torques
Large-Time Behavior of a Rigid Body of Arbitrary Shape in a Viscous Fluid Under the Action of Prescribed Forces and Torques
复制标题
粘性流体中任意形状刚体在规定力和扭矩作用下的长时间行为
DOI：
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发表时间：
2022
影响因子：
1.3
通讯作者：
G. Galdi
中科院分区：
文献类型：
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作者：
G. Galdi
设$${mathcal B}$$ B是在规定的外力$$F $$ F和扭矩$$M $$ M的作用下，在无界的Navier-Stokes液体中运动的任意形状的足够光滑的刚体（$${mathbb R}^3$$ R 3的紧化集）。我们证明，如果数据适当正则且小，并且$$F $$ F和$$M $$ M在$$L^2$$ l2意义下大量消失，则存在至少一个对应的初始边值问题的全局强解。而且，当时间趋于无穷时，这个解收敛于零。到目前为止，这种类型的结果是已知的，只有当$${mathcal B}$$ B是一个球。
Let $${mathcal B}$$ B be a sufficiently smooth rigid body (compact set of $${mathbb R}^3$$ R 3 ) of arbitrary shape moving in an unbounded Navier–Stokes liquid under the action of prescribed external force, $$F $$ F , and torque, $$M $$ M . We show that if the data are suitably regular and small, and $$F $$ F and $$M $$ M vanish for large times in the $$L^2$$ L 2 -sense, there exists at least one global strong solution to the corresponding initial-boundary value problem. Moreover, this solution converges to zero as time approaches infinity. This type of results was known, so far, only when $${mathcal B}$$ B is a ball.
DOI：
10.1090/s0002-9947-2012-05652-2
发表时间：
2012-08
影响因子：
1.3
作者：
M. Geissert;K. Götze;Matthias Hieber
通讯作者：
M. Geissert;K. Götze;Matthias Hieber