Problem of the motion of two compressible fluids separated by a closed free interface
Problem of the motion of two compressible fluids separated by a closed free interface
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由封闭自由界面分隔的两种可压缩流体的运动问题
DOI：
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发表时间：
2000
期刊：
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通讯作者：
I. Denisova
中科院分区：
文献类型：
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作者：
I. Denisova
考虑两种正压毛细粘性可压缩流体同时演化的问题，这两种正压毛细粘性可压缩流体占据空间，并被封闭的自由界面隔开。在一定粘度条件下，得到了该问题在Sobolev-Slobodetskii空间中的局部（时间上）唯一可解性。在过渡到拉格朗日坐标之后，可以从方程组中排除流体密度。摘要基于逐次逼近法和一类具有平面界面的线性模型问题的显式解，证明了一类非线性非强制初边值问题的存在性定理。上述对黏度的限制出现在具有指数权重的Sobolev空间的显式解的中间估计中。参考书目：8篇。
We consider the problem of the simultaneous evolution for two barotropic capillary viscous compressible fluids occupying the space ℝ3 and separated by a closed free interface. Under some restrictions on the viscosities of the liquids, the local (in time) unique solvability of this problem is obtained in the Sobolev-Slobodetskii spaces. After the passage to Lagrangian coordinates it is possible to exclude the fluid density from the system of equations. The proof of the existence theorem for a nonlinear, noncoercive initial boundary-value problem is based on the method of successive approximations and on an explicit solution of a model linear problem with a plane interface between the liquids. The restrictions on the viscosities mentioned above appear in the intermediate estimation of this explicit solution in the Sobolev spaces with an exponential weight. Bibliography: 8 titles.