Global solvability of a problem governing the motion of two incompressible capillary fluids in a container
Global solvability of a problem governing the motion of two incompressible capillary fluids in a container
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容器中两种不可压缩毛细管流体运动问题的全局可解性
DOI：
10.1007/s10958-012-0951-8
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发表时间：
2012
影响因子：
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通讯作者：
V. Solonnikov
中科院分区：
文献类型：
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作者：
I. Denisova;V. Solonnikov
我们处理容器中两个不可压缩流体的运动，其中一个在另一个容器内，考虑了表面张力。我们证明了当流体的初始速度很小，且内部流体的初始构形接近于球时，该问题在无限时间区间内是唯一可解的。此外，我们还证明了速度随时间呈指数衰减，并且流体之间的界面趋于某一半径的球体。证明基于广义能量的指数估计和各向异性Hölder空间中问题的局部存在定理。我们遵循其中一位作者提出的方案，证明了一个由自由面约束的不可压缩毛细流体运动问题的整体可解性。参考书目：18种。
We deal with the motion of two incompressible fluids in a container one of which is inside another, taking into account the surface tension. We prove that this problem is uniquely solvable in an infinite time interval provided that the initial velocity of the fluids is small and the initial configuration of the inner fluid is close to a ball. Moreover, we show that the velocity decays exponentially at infinity with respect to time and that the interface between the fluids tends to a sphere of a certain radius. The proof is based on an exponential estimate of a generalized energy and on a local existence theorem for the problem in anisotropic Hölder spaces. We follow the scheme developed by one of the authors for proving the global solvability of a problem governing the motion of one incompressible capillary fluid bounded by a free surface. Bibliography: 18 titles.
均匀旋转毛细管液体的稳定性
DOI：
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发表时间：
2022
期刊：
影响因子：
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作者：
赤尾 奏名汰;顧 玉杰;櫻井 幸一;Watanabe Keiichi;Watanabe Keiichi;Watanabe Keiichi;Watanabe Keiichi;Watanabe Keiichi;Watanabe Keiichi;渡邊圭市;渡邊圭市;渡邊圭市;Keiichi Watanabe
通讯作者：
Keiichi Watanabe